Chromatic aberration correcting element and its application

ABSTRACT

A chromatic aberration correcting element that is a simple lens having at least one aspheric surface, the radius of curvature of which increases from the optical axis toward the periphery. At least one of the surfaces is formed as a diffraction lens surface that consists of annular segments that shift discretely in a direction in which the lens thickness increases as a function of the distance from the optical axis. Also disclosed is a chromatic aberration correcting device having annular segments formed in steps on either a light entrance face or a light exit face or both. The annular segments are composed of planes perpendicular to and concentric with the optical axis.

This is a divisional of application Ser. No. 08/630,597 filed Apr. 10,1996 now U.S. Pat. No. 5,796,520 which is a divisional of applicationSer. No. 08/091,983 filed Jul. 16, 1993 now U.S. Pat. No. 5,629,799.

BACKGROUND OF THE INVENTION

The present invention relates to a lens that is capable of correctingchromatic aberration by itself. Also, the present invention relates to adevice for correcting the chromatic aberration inherent in opticalsystem. More particularly, the present invention relates to a chromaticaberration correcting device that is intended for use in combinationwith a single aspheric lens that is corrected for aberrations other thanchromatic ones.

The use of a single objective lens having an aspheric surface on bothsides has expanded these days in the art of optical disks and one of theprincipal reasons for this use is its contribution to weight reduction.However, the single lens in conventional use has been incapable ofeffective correction of chromatic aberration. A laser diode which isused as a light source for optical disks has the disadvantage that itsemission wavelength is shifted on account of the change either in theoutput power of the laser or in the temperature. Hence, if the objectivelens is not corrected for chromatic aberration, the focusing position oflight rays will change in response to the shift in wavelength and thiscan cause errors when reading or writing information.

To solve this problem, the present inventors previously proposedchromatic aberration correcting devices that had two or three glass lenselements cemented together (see Japanese Patent Public Disclosure Nos.Hei 3-155514 and 3-155515). By combining either one of these chromaticcorrecting devices with a single aspheric lens, one could offer a lenssystem that was immune to the effect of wavelength variations, requiringless lens elements than the conventional system that is effectivelycorrected for chromatic aberration.

However, the techniques proposed in the two patents cited above sufferfrom the disadvantage that in order to correct chromatic aberration, itis necessary to provide a device that is not directly concerned with thefocusing action inherent in the objective lens. Therefore, opticalsystem that is properly corrected for chromatic aberration weighs moreand requires more parts than optical system that is not corrected.

The conventional chromatic aberration correcting device has had theproblem that its manufacturing cost is so high as to cancel theadvantage of lower cost that results from the use of a single asphericlens, whereby the net benefit is reduced to nil.

The present invention has been accomplished under these circumstancesand has as an object providing a lens that utilizes diffraction effectso as to correct chromatic aberration effectively without undulyincreasing the number of lens elements.

The present invention has been accomplished under these circumstancesand has as an object providing a chromatic aberration correcting devicethat can be manufactured at a lower cost than devices that consist oftwo or three glass plates cemented together.

SUMMARY OF THE INVENTION

In order to meet the above-described requirement, according to thepresent invention, there is provided a single chromatic aberrationcorrecting lens that is a single lens having at least one asphericsurface the radius of curvature of which increases from the optical axistoward the periphery, at least either one of the surfaces being formedas a diffractive lens surface that consists of annular segments in stepsthat are shifted discretely in a direction in which the lens thicknessincreases as a function of the distance from the optical axis.

The single chromatic aberration correcting lens satisfies the followingcondition:

    0.8≦t(n-1)/λ.sub.0 ≦10

where λ₀ : arbitrary wavelength in the operating wavelength;

t: the amount of axial shift of each annular segment (difference inheight between adjacent steps);

n: the refractive index of the medium of which the lens is made.

The diffractive lens surface is provided by the surface closer to thefar conjugate point whereas a continuous aspheric surface is provided bythe surface closer to the near conjugate point, the diffractive lenssurface being formed in steps as annular segments that are shifteddiscretely on a pitch that is substantially in inverse proportion to thesquare of the height from the optical axis.

The correcting lens according to the present invention may be providedin the optical system of an optical information recording andreproducing apparatus and which functions as an objective lens thatcauses incident parallel rays of light coming from the side closer tothe far conjugate point to be focused on an optical recording medium.

Alternatively, the diffractive lens surface is provided by the surfacecloser to the near conjugate point whereas a continuous aspheric surfaceis provided by the surface closer to the far conjugate point, thediffractive lens surface being formed in steps as annular segments thatare shifted discretely on a pitch that is substantially in inverseproportion to the square of the height from the optical axis.

According to another aspect of the invention, there is provided achromatic aberration correcting device having annular segments formed insteps on either a light entrance face or a light exit surface or both,the annular segments being composed of planes perpendicular to andconcentric with the optical axis.

The shift amount in the optical direction of adjacent annular zone t ofthe planes defined by the following condition:

    t=mλ.sub.0 /(n-1)

where m is an integer, n is the refractive index, and λ10 is anarbitrary wavelength in the operating wavelength range.

The surface on which the step-like annular segments are formed ismacroscopically a concave surface.

Alternatively, the surface on which the step-like annular segments areformed is macroscopically a convex surface.

According to the invention, in an optical information recording andreproducing apparatus that allows beams of light from a light source tobe focused on an information recording medium by means of an objectivelens so as to record or reproduce information, the improvement wherein achromatic aberration correcting device is provided in the optical pathbetween the light source and the objective lens, the chromaticaberration correcting device having annular segments formed in steps oneither a light entrance surface or a light exit surface or both, theannular segments being composed of planes perpendicular to andconcentric with the optical axis.

According to another aspect of the invention, in a chromatic aberrationcorrecting device of a diffraction type that has annular segments formedin steps on either a light entrance surface or a light exit surface orboth, the annular segments being composed of planes perpendicular andconcentric with the optical axis, the improvement wherein the base curvewhich is a macroscopic curvature of the planes formed in steps is anaspheric surface the radius of curvature of which decreases in absolutevalue with the increasing distance from the optical axis and, when theaxial displacement of the base curve at a point having distance h fromthe optical axis is written as ΔX(h), the displacement ΔX' (h) of theplanes formed in steps at a point having distance h from the opticalaxis is given by equation (3B):

    ΔX'(h)=(mλ.sub.0 /(n-1))Int((ΔX(h)/mλ.sub.0 /(n-1)))+0.5)                                             (3B)

where m is an integer; n is the refractive index; λ₀ is the wavelengthat which the chromatic aberration correcting device is used or anarbitrary wavelength within the operating wavelength range of thedevice; and Int(X) is a function giving an integer not greater than X.

The base curve is an aspheric surface resembling a spheroidal surfacehaving a positive conic constant and, when the departure ε(h) from thespheroidal surface at a point having distance h from the optical axis isexpressed by equation (1B), the base curve satisfies condition (4B) atall values of distance h within the effective maximum radius of passingbeams of light: ##EQU1## where C is the paraxial curvature; K is theconic constant; and λ is the maximum operating wavelength.

Optical system for an optical information recording and reproducingapparatus comprises:

a light source;

an objective lens that causes beams of light from the light source to befocused on an optical recording medium; and

a beam splitter by means of which the reflected light from the opticalrecording medium is isolated from the optical path of incident lightbeams;

the beam splitter having a surface that generates chromatic aberrationwhich at least cancels the chromatic aberration that develops in theobjective lens.

According to the present invention, optical system for an opticalinformation recording and reproducing apparatus at least comprises:

a light source;

an optical path deflecting means that causes beams of light from thelight source to be deflected toward an optical recording medium;

an objective lens that causes the deflected light beams to be focused onthe optical recording medium;

a beam splitter by means of which the reflected light from the opticalrecording medium is isolated from the optical path of incident lightbeams;

the optical path deflecting means having a surface that generateschromatic aberration which at least cancels the chromatic aberrationthat develops in the objective lens.

According to the present invention, a chromatic aberration correctingdevice having at least one prism and annular planes concentric with theoptical axis being formed in steps on at least one of the beam passingsurfaces of the prism in such a way that the annular planes produce amacroscopically concave shape, chromatic aberration being generated bythe step-like planes.

According to another aspect of the invention, a hybrid lens thatcomprises:

a glass lens having a refractive action; and

a plastic diffraction element one surface of which is joined to theglass lens and the other surface of which is provided with a pluralityof annular planes that are concentric with the optical axis and whichare formed in steps in such a way that the lens thickness increases as afunction of the distance from the optical axis.

The hybrid lens may further satisfy the following condition:

    0.8≦t(n-1)/λ.sub.0 ≦10

where λ₀ : arbitrary wavelength in the operating wavelength;

t: the axial difference in the thickness of the diffraction elementbetween individual annular segments; and

n: the refractive index of the medium of which the diffraction elementis made.

According to still another aspect of the invention, there is provided achromatic aberration correcting device of a reflection and diffractiontype that has a reflecting surface comprising the central reflectingsurface and a plurality of annular reflecting surfaces that areconcentric with the central reflecting surface, the reflecting surfacesbeing such that the shapes of their orthogonal projections onto a planeperpendicular to the optical axis are characterized by rotation symmetrywith respect to the optical axis serving as the center of rotation, thecentral reflecting surface, an annular reflecting surface just outwardof the central reflecting surface and an adjacent annular reflectingsurface being offset in position by the same step distance t in adirection perpendicular to those reflecting surfaces, so that when seenmacroscopically, those reflecting surfaces provide a concave or a convexsurface as a whole, the step distance t being specified in such a waythat light entering as a plane wave at a reference wavelength will alsoemerge as a plane wave whereas light entering as a plane wave at awavelength different from the reference wavelength will emerge as eithera divergent or a convergent wavefront.

BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings:

FIG. 1 shows schematically optical system in a case where the singlechromatic aberration correcting lens according to Example 1 of thepresent invention is used as an objective lens of an infinite system inan optical disk apparatus;

FIG. 2(a) is a cross section showing the objective lens of FIG. 1 in anexaggerated form;

FIG. 2(b) is a plan view of the same objective lens in an exaggeratedform;

FIG. 3 is a set of graphs plotting the aberrations curves that areobtained with the optical system shown in FIG. 1;

FIG. 4 shows schematically optical system in a case where the singlechromatic aberration correcting lens according to Example 2 of thepresent invention is used as a collimator lens;

FIG. 5(a) is a cross section showing the collimator lens of FIG. 4 in anexaggerated form;

FIG. 5(b) is a plan view of the same collimator lens in an exaggeratedform;

FIG. 6 is a set of graphs plotting the aberration curves obtained withthe optical system shown in FIG. 4;

FIG. 7 shows schematically optical system in a case where the singlechromatic aberration correcting lens according to Example 3 of thepresent invention is used as an objective lens of a finite system in anoptical disk apparatus;

FIG. 8 is a set of graphs plotting the aberration curves obtained withthe optical system shown in FIG. 7;

FIG. 9 is a cross section showing an example of the chromatic aberrationcorrecting device of the present invention as it is taken on line IX--IXof FIG. 10;

FIG. 10 is a plan view of the device shown in FIG. 9;

FIG. 11 is a diagram showing the wavefront of light as it passes throughthe chromatic aberration correcting device at the design wavelength;

FIG. 12 is a diagram showing the wavefront of light as it passes throughthe chromatic aberration correcting device at a wavelength other thanthe design wavelength;

FIG. 13 shows schematically the case in which the chromatic aberrationcorrecting device is combined with an objective lens;

FIG. 14 shows schematically the case in which the chromatic aberrationcorrecting device is macroscopically shaped like a biconcave lens;

FIG. 15 shows schematically the case in which the chromatic aberrationcorrecting device is macroscopically shaped like a convexo-plane lens;

FIG. 16 shows schematically the case in which the chromatic aberrationcorrecting device is macroscopically shaped like a biconvex lens;

FIG. 17 shows schematically an example of optical system in an opticalinformation recording and reproducing apparatus including the chromaticaberration correcting device;

FIG. 18 shows schematically another example of optical system in anoptical information recording and reproducing apparatus including thechromatic aberration correcting device;

FIG. 19 is a simplified diagram showing schematically a positiveobjective lens that is to be corrected by the chromatic aberrationcorrecting devices of Examples 1B to 3B;

FIG. 20 is a set of graphs plotting the spherical and chromaticaberration curves obtained with the objective lens alone that is shownin FIG. 19;

FIG. 21 is a simplified diagram showing schematically optical system inwhich the lens shown in FIG. 19 is combined with the refractive-typechromatic aberration correcting device of Example 1B in which thecemented surface is ellipsoidal;

FIG. 22 is a set of graphs plotting the spherical and chromaticaberration curves obtained with the optical system shown in FIG. 21;

FIG. 23 is a simplified diagram showing schematically optical system inwhich the objective lens shown in FIG. 19 is combined with arefractive-type chromatic aberration correcting device in which thecemented surface is spherical;

FIG. 24 is a set of graphs plotting the spherical and chromaticaberration curves obtained with the optical system shown in FIG. 23;

FIG. 25 is a simplified diagram showing schematically optical system inwhich the lens shown in FIG. 19 is combined with a diffraction-typechromatic aberration correcting device;

FIGS. 26A and 26B are a side view and a plan respectively, that showschematically the geometry of step-like planes formed on thediffraction-type chromatic aberration correcting device;

FIG. 27 is a set of graphs plotting the spherical and chromaticaberration curves obtained with the optical system shown in FIG. 25 forthe case of using the diffraction-type chromatic aberration correctingdevice of Example 2B in which the base curve for the step-like planesprovides an ellipsoidal surface;

FIG. 28 is a set of graphs plotting the spherical and chromaticaberration curves obtained with the optical system shown in FIG. 25 forthe case of using the diffraction-type chromatic aberration correctingdevice of Example 3B in which the base curve for the step-like planesprovides a fourth-order aspheric surface;

FIG. 29 is a set of graphs plotting the spherical and chromaticaberration curves obtained with the optical system shown in FIG. 25 forthe case of using a diffraction-type chromatic aberration correctingdevice in which the base curve for the step-like planes provides aspherical surface;

FIG. 30 is a simplified diagram showing schematically the positiveobjective lens that is to be corrected by the chromatic aberrationcorrecting devices of Examples 4B and 5B;

FIG. 31 is a set of graphs plotting the spherical and chromaticaberration curves obtained with the objective lens alone that is shownin FIG. 30;

FIG. 32 is a simplified diagram showing schematically optical system inwhich the objective lens shown in FIG. 30 is combined with arefractive-type chromatic aberration correcting device in which thecemented surface is spherical;

FIG. 33 is a set of graphs plotting the spherical and chromaticaberration curves obtained with the optical system shown in FIG. 32;

FIG. 34 is a simplified diagram showing schematically optical system inwhich the lens shown in FIG. 30 is combined with the refractive-typechromatic aberration correcting device of Example 4B in which thecemented surface is ellipsoidal;

FIG. 35 is a set of graphs plotting the spherical and chromaticaberration curves obtained with the optical system shown in FIG. 34;

FIG. 36 is a simplified diagram showing schematically optical system inwhich the lens shown in FIG. 30 is combined with a diffraction-typechromatic aberration correcting device;

FIG. 37 is a set of graphs plotting the spherical and chromaticaberration curves obtained with the optical system shown in FIG. 36 forthe case of using the diffraction-type chromatic aberration correctingdevice of Example 5B in which the base curve for the step-like planesprovides an ellipsoidal surface;

FIG. 38 is a set of graphs plotting the spherical and chromaticaberration curves obtained with the optical system shown in FIG. 36 forthe case of using a diffraction-type chromatic aberration correctingdevice in which the base curve for the step-like planes provides aspherical surface;

FIG. 39 is a simplified diagram showing schematically the optical systemfor optical information recording and reproducing apparatus according toExample 1C;

FIG. 40 is a simplified diagram showing a modification of the opticalsystem shown in FIG. 39;

FIG. 41 is a simplified diagram showing schematically the optical systemfor optical information recording and reproducing apparatus according toExample 2C;

FIG. 42 is a plan view showing the optical system for opticalinformation recording and reproducing apparatus according to Example 3C;

FIG. 43 is a side view showing the same optical system according toExample 3C;

FIG. 44 is a simplified diagram showing schematically the optical systemfor optical information recording and reproducing apparatus according toExample 4C;

FIG. 45 is a simplified diagram showing schematically the optical systemfor optical information recording and reproducing apparatus according toExample 5C;

FIG. 46A is a side view showing schematically the hybrid lens accordingto the examples of the present invention;

FIG. 46B is a plan view of the same hybrid lens;

FIG. 47 is a simplified diagram showing schematically an objective lensthat uses the hybrid lens of Example 1D;

FIG. 48 is a set of graphs plotting the aberration curves obtained withthe objective lens shown in FIG. 47;

FIG. 49 is a simplified diagram showing schematically an objective lensthat uses the hybrid lens of Example 2D;

FIG. 50 is a set of graphs plotting the aberration curves obtained withthe objective lens shown in FIG. 49;

FIG. 51 is a simplified diagram showing schematically an objective lensthat is a comparison with Example 2D in that it does not have adiffraction element;

FIG. 52 is a set of graphs plotting the aberration curves obtained withthe objective lens shown in FIG. 51;

FIG. 53 is a simplified diagram showing schematically a collimator lensthat uses the hybrid lens of Example 3D;

FIG. 54 is a set of graphs plotting the aberration curves obtained withthe collimator lens shown in FIG. 53;

FIG. 55 is a simplified diagram showing schematically a telephoto lenssystem that uses the hybrid lens of Example 4D;

FIG. 56 is a set of graphs plotting the aberration curves obtained withthe telephoto lens system shown in FIG. 55;

FIG. 57 is simplified diagram showing schematically a telephoto lenssystem that is a modification of Example 4D in that it has a diffractionelement provided on a filter;

FIG. 58 is a simplified diagram showing schematically a telephoto lenssystem that is a comparison with Example 4D in that it does not have adiffraction element;

FIG. 59 is a set of graphs plotting the aberration curves obtained withthe telephoto lens system shown in FIG. 58;

FIG. 60 is a cross-sectional view illustrating the operating principleof the chromatic aberration correcting device of a reflection anddiffraction type according to one embodiment of the present invention;

FIG. 61 is another cross-sectional view that also illustrates theoperating principle of the chromatic aberration correcting device of areflection and diffraction type according to the present invention;

FIG. 62 is a cross-sectional view showing the operating principle of thechromatic aberration correcting device of a reflection and diffractiontype according to another embodiment of the present invention;

FIG. 63 is a section of FIG. 62 as it is seen in the direction indicatedby arrow A;

FIG. 64 is a perspective view showing an embodiment of the presentinvention in which the chromatic aberration correcting device of areflection and diffraction type is applied to an optical informationrecording and reproducing apparatus;

FIG. 65 is a cross-sectional view showing the first example of thechromatic aberration correcting device of a reflection and diffractiontype according to the present invention;

FIG. 66 is a cross-sectional view showing the second example of thechromatic aberration correcting device of a reflection and diffractiontype according to the present invention;

FIG. 67 is a cross-sectional view showing the third example of thechromatic aberration correcting device of a reflection and diffractiontype according to the present invention;

FIG. 68 is a cross-sectional view showing the fourth example of thechromatic aberration correcting device of a reflection and diffractiontype according to the present invention;

FIG. 69 shows schematically the chromatic aberration that develops in asingle lens and how it is corrected by the chromatic aberrationcorrecting device of a reflection and diffraction type according to thepresent invention;

FIG. 70 is a simplified diagram showing an example of the single lensthat is to be used in combination with the chromatic aberrationcorrecting device of a reflection and diffraction type according to thepresent invention;

FIG. 71 is a set of graphs plotting the aberration curves obtained withthe single lens shown in FIG. 70;

FIG. 72 is a diagram showing another lens system to which the chromaticaberration correcting device of a reflection and diffraction typeaccording to the present invention is to be applied; and

FIG. 73 is a set of graphs plotting the aberration curves obtained withthe lens system shown in FIG. 72.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Embodiments of the single chromatic aberration correcting lens accordingto the present invention are described below. First, let us describe theoperating theory of the invention.

Suppose a thin lens having a focal length of f that is made from amaterial having a refractive index n which varies by Δn in response tothe change in wavelength. The change in the power of this lens ΔR inresponse to the change in wavelength is expressed by the followingequation (1):

    ΔR=Δn/(f(n-1))                                 (1)

In the absence of a material that has a sufficient refractive index n tomake a lens and which yet experiences only a small index change Δn, noordinary single lens having power is capable of suppressing the powerchange ΔR that occurs as a result of this change in wavelength.

Under the circumstances, the single chromatic aberration correcting lensof the present invention is adapted to form a diffractive lens surfaceon either one of the surfaces of a single lens in such a way that thediffractive action of that surface is effectively used to cancel thechromatic aberration that will develop on account of the refractiveaction of the single lens.

A diffractive lens may be available as either an amplitude diffractionor a phase diffractive lens depending upon the type of diffraction thatoccurs. From the viewpoint of efficient light utilization, a phasediffractive lens is desirably used. The phase diffractive lens is formedby providing a series of annular segments in steps that are planesperpendicular to and concentric with the optical axis.

If the refractive power of a lens is written as φR and if the power of adiffractive lens surface formed on one surface of that lens is writtenas φD, the composite power φT is expressed by the following equation(2):

    φT=(HR/H1)φR+(HD/H1)φD                         (2)

where H1: the height of a paraxial ray at which it enters the lenssystem;

HR: the height of the H1 incident paraxial ray at which it enters therefractive lens on the front principal point;

HD: the height of the H1 incident paraxial ray at which it enters thediffractive lens on the front principal point.

For the sake of simplicity, let each lens be assumed as a thin lens.Then, equation (2) can be rewritten as follows:

    φT=φR+φD                                       (3)

With an ordinary refractive lens, the change in lens power ΔR that iscaused by the index change Δn due to a variation in wavelength isexpressed by equation (4):

    ΔR=φR(Δn/(n-1))                            (4)

where φR is the refractive power of the lens.

The power of a diffractive lens surface φD is calculated by taking thedifferential coefficient of second order of the optical pathlengthdifference (as caused by diffraction) with respect to the distance fromthe optical axis. Since the optical pathlength difference isproportional to wavelength, the power change ΔD due to the diffractionthat occurs when the wavelength is shifted by Δλ from the designreference value λ₀ is expressed by the following equation (5):

    ΔD=(Δλ/λ.sub.0)φD            (5)

Suppose here that a lens having a focal length of 10 mm that is to beoperated with a laser diode emitting light at a reference wavelength(λ₀) of 780 nm with a shift (Δλ) of ±10 nm is fabricated from LAL 13(trade name of Ohara Co., Ltd.; n780=1.68468; Δn=-0.000032). Equations(4) and (5) give the following values:

    ΔR=φR(Δn/(n-1))=-4.67×10.sup.-4 ·φR

    ΔD=φD(Δλ/λ.sub.0)=1.28×10.sup.-2 ·φD

In order to suppress the variation in composite power due to thedifference in wavelength, ΔR and ΔD may be so set that their sum is zero(ΔR+ΔD=0). In other words, a lens that is free from chromatic aberrationat wavelengths near the reference value 780 nm can be fabricated bysatisfying the following condition (7):

    φR:φD=1:0.0364                                     (7)

Further, in order to insure the focal length 10 mm, the followingequation (8) must hold:

    φR+φD=0.100                                        (8)

Equations (7) and (8) show that the refractive and diffractive powersare respectively expressed by the following equations (9) and (10):

    φR=0.09649                                             (9)

    φD=0.00351                                             (10)

By the second integration of equation (10) with respect to the distancefrom the optical axis, the optical pathlength difference OPD(h) at thepoint on the diffractive lens surface that departs from the optical axisby height h is determined as follows: ##EQU2##

It should be noted here that in order to develop diffraction, theoptical pathlength difference must be varied not continuously butintermittently or discretely in steps. Stated more specifically, theoptical pathlength difference that occurs between light passing througha medium with the thickness t along the optical path and light passingthrough air is given by (n-1)t and, hence, the difference in heightbetween adjacent steps on the diffractive lens must be t which is givenby the following equation (12), or an integral multiple of the same:

    t(h)=0.780×10.sup.-3 / (n-1)=0.780×10.sup.-3 /0.68468=1.14×10.sup.-3 *h.sup.2                    (12)

Therefore, macroscopically, the diffractive lens is shaped like aconcave lens the thickness of which increases in proportion to thesquare of the distance from the optical axis but, microscopically,annular segments are formed in steps concentric with the optical axis inthe manner already defined hereinabove. By meeting these requirements,the diffractive lens can provide a desired power.

The foregoing discussion assumes that the single chromatic aberrationcorrecting lens of the present invention is a thin lens and that,therefore, the height of ray incidence does not change on the twosurfaces of the lens. In practice, however, the height of ray incidencediffers between the front and rear surfaces of the lens and, hence, thechange in h must also be taken into consideration.

It should also be noted that the ratio between the optical pathlengthdifference t(n-1) and the wavelength λ₀ desirably satisfies thefollowing condition (A):

    0.8≦t(n-1)/λ.sub.0 ≦10                (A)

It is generally held that if a diffractive lens surface is formed insuch a way that the difference in height between adjacent steps is equalto the wavelength λ₀, one will use light of first-order diffraction and,hence, is capable of suppressing the deterioration in wavefrontaberration due to the change in wavelength, thereby preventing the dropin diffraction efficiency and imaging performance which would other-wiseoccur on account of the wavelength change.

If the operating wavelength range is narrow or in a case like that wherethe width of each annular segment is small enough to present difficultyin lens manufacture, the difference in height between adjacent steps maybe increased to twice the wavelength or an integral multiple (≦3) of thesame and, yet, it is possible to perform the correction of chromaticaberration. However, if the difference in height between steps exceedsthe upper limit of condition (A) and becomes greater than ten times thewavelength λ, the lens geometry will be no different from theconventional Fresnel lens and the following two problems will occur: dueto a possible manufacturing error in the difference in height betweensteps, there is high likelihood of increased phase mismatching and,secondly, the efficiency of the diffractive lens decreases if theincident light has a wavelength departing from the design value.

If, on the other hand, the lower limit of condition (A) is not reached,the phase matching necessary for the diffractive lens cannot beaccomplished and it is substantially incapable of working as a"diffractive" lens.

If the diffractive lens and the refractive lens are to be combined in anintegral unit for the purpose of correcting chromatic aberration, almostall the power that develops is created by the refractive lens asequation (7) shows. Therefore, it is necessary that the refractive lensbe adapted to be capable of substantial correction of aberrations byitself. On the other hand, the power of the diffractive lens is almostnil since its sole function is to correct the chromatic aberration thatdevelops in the refractive lens. Therefore, the single chromaticaberration correcting lens as an integral unit has no marked differencefrom the conventional single aspheric lens as far as the macroscopicgeometry is concerned.

EXAMPLE 1

FIG. 1 shows optical system that uses a single chromatic aberrationcorrecting lens according to Example 1 of the present invention, inwhich the lens is used as an objective lens in an optical disk system.Beams of parallel light entering the lens 1 from the left are focused toform a spot on the recording surface located on the inner (right) sideof the cover glass D of the optical disk. The lens 1 is an objectivelens both surfaces of which are macroscopically convex.

FIGS. 2(a) and 2(b) are a cross section and a plan view, respectively,that show the objective lens 1 as it is exaggerated to clarify thegeometry of the annular segments formed on it. The left side of lens 1(as seen in FIG. 2(a)) on which the parallel light is to be incidentprovides a discontinuous surface that is the combination of an asphericsurface of a refractive lens with annular segments that are formed on itto create a surface working as a diffractive lens surface. The annularsegments are formed concentrically in steps that are shifted discretelyin a direction in which the lens thickness increases as a function ofthe distance from the optical axis. The side of the lens 1 that facesthe cover glass D forms an ordinary continuous aspheric surface.

In order to correct spherical aberration and coma at the same time inthe case where a high NA (numerical aperture) lens like the objectivelens in an optical disk system is composed of a single lens, the surfaceon the side where parallel beams of light are incident, namely, on theside at the far conjugate point, must be formed as a convex asphericsurface the radius of curvature of which increases from the optical axistoward the periphery.

In order for a lens to be bright, the sine condition for coma correctionmust be substantially satisfied. Hence, when combining a high NA lenswith the diffractive lens, the optical pathlength that should beprovided by the latter is not proportional to the square of the heightof ray incidence h, but proportional to the square of the sine of theincident or emerging angle. Therefore, except in the case where thediffractive lens surface is on the sides where the parallel light entersand emerges, the geometry of the diffractive lens surface must be suchthat its curvature is not strictly proportional to the square ofdistance h from the optical axis but decreases gradually toward theperiphery. It should also be noted that if the incident ray enters thediffractive lens at an angle (obliquely), the effective lens thicknesswill increase; therefore, in the case where the diffractive lens islocated on the side of the high NA lens that is closer to the exitsurface, the amount of shift must also be considered as a function of h.

If the diffractive lens to be combined in a unitary assembly is locatedat the far conjugate point as in the case of Example 1, the incidentrays are subjected to the angle varying action on the diffractive lenssurface in the axial direction and, hence, the difference in heightbetween angular steps on the diffractive lens surface will increase fromthe optical axis toward the periphery. However, it is difficult tomanufacture a system in which the lens surface is shifted in thedirection in which the rays travel; therefore, in the actualmanufacturing operation, the lens surface may be shifted in the axialdirection.

The specific numerical data for Example 1 are listed in Tables 1 to 3below. FIG. 3 shows the three aberrations that develop in the systemcomposed in accordance with those data: coma, chromatic aberrationexpressed in terms of spherical aberrations at 770 nm, 780 nm and 790nm, and astigmatism (S, sagittal; M, meridional).

                  TABLE 1    ______________________________________    Reference wavelength                       λ.sub.0                                 780 nm    Focal length       f         3.30 mm    Numerical aperture NA        0.55    Lens quality       n780      1.53677                       Δn  0.000025/nm    Lens thickness     t         2.21 mm    Disk thickness     tD        1.20 mm    Refractive index of disk                       nD        1.57346    ______________________________________

The shape of the first surface of the single chromatic aberrationcorrecting lens is given by the coefficients listed in Table 2 (seebelow) if the sag X(h) of the aspheric surface at the point that isseparated from the optical axis by distance h is defined by thefollowing equation (13) which has the term ΔN added to the commonexpression of aspheric surrace. Symbol INT(x) in Table 2 denotes afunction for separating out the integral part of ##EQU3## where r is theradius of curvature of the vertex of the aspheric surface; N is thenumber for the annular segment to which the point at height h belongs; Kis the conic constant; and A4, A6, A8 and A10 are the asphericcoefficients of the fourth, sixth, eighth and tenth orders,respectively.

                  TABLE 2    ______________________________________           N =   INT(4.71 * h.sup.2 + 0.5)           rN =    2.126 + 5.09 × 10.sup.-4 * N           KN =  -0.3689           A4N = -1.470 × 10.sup.-3 + 1.45 × 10.sup.-6 * N           A6N = -2.180 × 10.sup.-4 + 8.72 × 10.sup.-8 * N           A8N = -1.000 × 10.sup.-5 + 4.36 × 10.sup.-8 * N           A10N =                 -1.400 × 10.sup.-5 + 3.49 × 10.sup.-8 * N           ΔN =                 -0.001453 * N    ______________________________________

The shape of the second surface of the single chromatic aberrationcorrecting lens 1 is given by the coefficients listed in Table 3 (seebelow) if the aspheric surface is defined by equation (14): ##EQU4##

                  TABLE 3    ______________________________________              r =   -6.763              K =     0.000              A4 =    1.777 × 10.sup.-2              A6 =  -3.950 × 10.sup.-3              A8 =    5.770 × 10.sup.-4              A10 = -2.960 × 10.sup.-5    ______________________________________

EXAMPLE 2

FIG. 4 shows the case where the single chromatic aberration correctinglens according to Example 2 of the present invention is used as acollimator lens which collimates the divergent light from a laser diode.The collimator lens indicated by 2 has a meniscus shape which, as seenmacroscopically, is convex on the left side from which beams of thecollimated light emerge.

FIGS. 5(a) and 5 (b) are a cross section and a plan view, respectively,that show the collimator lens 2 as it is exaggerated to clarify thegeometry of the annular segments formed on it. The right side of lens 2(as seen in FIG. 5(a)) which faces the cover glass 3 of the laser diodeprovides a discontinuous surface that has annular segments formed on itto create a surface working as a substantially powerless diffractivelens surface. The annular segments are formed concentrically in stepsthat are shifted discretely in a direction in which the lens thicknessincreases as a function of the distance from the optical axis. The leftside of the lens 2 from which beams of collimated light emerge forms anordinary continuous aspheric surface.

In a case like that of Example 2 where a diffractive lens surface isformed on the side closer to the near conjugate point, one may employ anoptical material having a refractive index ranging from 1.65 to 1.80.With such material, both spherical aberration and coma can be correctedby rendering only one surface aspheric whereas the other surface is leftpowerless. Thus, the diffractive lens surface can be formed on the basisof a plane and this facilitates the preparation of a lens forming mold.

If the refractive index is not within the range 1.65 to 1.80, it isdifficult to correct both spherical aberration and coma by means of aplane diffractive lens surface and some part of coma will remainuncorrected. Hence, the lens having an index outside the above-specifiedrange is not suitable for use as a high NA lens.

The specific numerical data for Example 2 are listed in Tables 4 and 5below. The shape of the first surface of collimator lens 2 which is onthe left side as seen in FIG. 4 is given by equation (14) (seeExample 1) into which the values listed in Table 5 are substituted. FIG.6 shows the three aberrations that develop in the system composed inaccordance with the data listed in Tables 4 and 5: coma, chromaticaberration expressed in terms of spherical aberrations, and astigmatism.

                  TABLE 4    ______________________________________    Reference wavelength                      λ.sub.0                                780 nm    Focal length      f         10.8 mm    Numerical aperture                      NA        0.20    Lens quality      n780      1.66959                      Δn  0.000030/nm    Lens thickness    t         2.50 mm    Cover glass thickness                      tC        0.25 mm    Refractive index of                      nC        1.51072    cover glass    ______________________________________

                  TABLE 5    ______________________________________              r =     7.231              K =   -0.5933              A4 =    0.000              A6 =  -3.440 × 10.sup.-7              A8 =  -4.370 × 10.sup.-9              A10 =   0.000    ______________________________________

The shape of the second surface of the single chromatic aberrationcorrecting lens is given by the following equation (15) in terms ofX(h), or the sag at the point that is separated from the optical axis bydistance h:

    X(h)=ΔN                                              (15)

where N is the number for the annular segment to which the point atheight h belongs and the asphericity-describing coefficient is thefollowing function of N:

    N=INT(2.70*h.sup.2 -0.0318*h.sup.4 +0.5)ΔN=0.001165*N

EXAMPLE 3

FIG. 7 shows optical system in which the single chromatic aberrationcorrecting lens according to Example 3 of the present invention is usedas an objective lens of a finite system for an optical disk. A laserbeam from a laser light source (not shown) passes through a substrate 4from the left and enters an objective lens 5 as divergent light, whichis focused by that objective lens 5 to form a spot on the back side ofthe cover glass D of the optical disk. An optical decoupling hologram orthe like is formed on the substrate 4.

The left side of objective lens 5 comprises an aspheric surface havingannular segments formed in steps to provide a diffractive lens surface,and the right side of the objective lens 5 provides a continuousaspheric surface.

A bright objective lens of the finite system that is shown in Example 3has a strong power or it must handle light at varying wavelength thatare not close to each other. In these cases, the refractive lens alonewill experience wavelength-dependent changes not only in focal positionbut also in the amount of spherical aberration; however, the diffractivelens can be used to produce spherical aberrations that are sufficient tocancel those changes in spherical aberration.

In a wavelength range near visible light, it can generally be the thatthe spherical aberration in a positive lens that is properly correctedat the reference wavelength will be under-corrected with respect toshorter-wavelength light which experiences higher refractive indexwhereas it is overcorrected with respect to longer-wavelength lightwhich experiences lower refractive index.

Therefore, in order to cancel the change that occurs in sphericalaberration on account of such variations in wavelength, the geometry ofthe diffractive lens may be so set that its power will increasegradually toward the periphery. The change in a lower-order sphericalaberration can be expressed in a biquadratic function in terms ofwavefront aberration; therefore, one can also suppress the variations inspherical aberration due to wavelength changes by defining the shape ofthe diffractive lens in terms of a function of two parts, one beingproportional to the square of h and the other being proportional to thefourth power of h.

The specific numerical data for Example 3 are listed in Tables 6 to 8below. The shape of the first surface of the objective lens 5 which ison the left side as seen in FIG. 7 is given by equation (13) (seeExample 1) into which the values listed in Table 8 are substituted. FIG.8 shows the three aberrations that develop in the system composed inaccordance with the data listed in Tables 6 to 8: coma, chromaticaberration expressed in terms of spherical aberrations, and astigmatism.

                  TABLE 6    ______________________________________    Reference wavelength                       λ.sub.0                                 780 nm    Magnification      m         -0.250    Focal length       f         2.64 mm    Object-to-image distance                       IO        17.76 mm    Numerical aperture NA        0.55    Lens quality       n780      1.53677                       Δn  0.000025/nm    Lens thickness     t         2.00 mm    Cover glass thickness                       tC        1.00 mm    Refractive index of                       nC        1.51072    cover glass    Disk thickness     tD        1.20 mm    Refractive index of disk                       nD        1.57346    ______________________________________

                  TABLE 7    ______________________________________    N =         INT(7.54 * h.sup.2 + 0.161 * h.sup.4 + 0.5)    rN =          1.939 + 1.95 × 10.sup.-4 * N    KN =        -0.4290 + 6.90 × 10.sup.-5 * N    A4N =       -8.120 × 10.sup.-3 + 6.90 × 10.sup.-7 * N    A6N =       -3.900 × 10.sup.-4 - 2.07 × 10.sup.-7 * N    A8N =       -8.260 × 10.sup.-5 + 1.45 × 10.sup.-7 * N    A10N =      -1.910 × 10.sup.-5 - 1.03 × 10.sup.-8 * N    ΔN =  -0.001453 * N    ______________________________________

                  TABLE 8    ______________________________________              r =   -3.377              K =     0.000              A4 =    2.768 × 10.sup.-2              A6 =  -4.261 × 10.sup.3              A8 =    5.157 × 10.sup.-4              A10 = -1.940 × 10.sup.-5    ______________________________________

As described on the foregoing pages, the present invention enables asingle aspheric lens to correct chromatic aberration while suppressingother aberrations such as spherical aberration and coma. Therefore, ifthis lens is used as an objective lens, it offers the advantage that itssize and weight are not much different from those of the prior artaspheric objective lens and that it yet is capable of correctingchromatic aberration to suppress defocusing that will occur on accountof variations in the wavelength of the light source used.

If a diffractive lens surface is formed on the side closer to the farconjugate point, namely, on the side where beams of parallel light enterwhen the lens of the invention is used as an objective lens for anoptical disk, one can avoid the deposition of dirt or dust that iscarried by an air stream generated by the revolving optical disk.Conversely, if a diffractive lens surface is to be formed on the sidecloser to the near conjugate point when the lens of the invention isused as a collimator lens, the diffractive lens surface can be formed ona substantially powerless side by properly selecting the refractiveindex of the optical material used. In this case, the diffractive lenssurface may assume a single shape that is just shifted from a planesurface and, hence, it can be manufactured easily.

Various examples of the present invention are described below.

A chromatic aberration correcting device according to an example of thepresent invention is shown in FIG. 9.

A chromatic correction element is provided with a central surface havinga revolution center about the optical axis and a plurality of annularzone surfaces which are coaxial with the central surface. The positionsof the central surface, the zonal surfaces outside of the centralsurface and the adjacent annular zonal surfaces are displaced by aconstant step distance t, so that these surfaces constitute a convexsurface or a concave surface in a macroscopic manner. The step distancet is determined so that rays of light which are introduced as planarwaves relative to a reference wave length light are emitted as planarwaves, and when rays of light which are different from the referencewave length light in wavelength, the rays of light which have beenintroduced as planar waves are emitted as divergent or convergent wavesurfaces. The width of each annular zone is preferably set to a valuewhich is in reverse proportion to the square of the distance from theoptical axis. With this dimension, in the case of the wavelengthvariation, it is possible to make the generated wave surfacesubstantially spherical.

The device is generally indicated by 101 and has a plurality ofstep-like planes formed on the light entrance surface 101a which is onthe left side whereas the exit surface 101b is composed of a singleplane. The planes at the entrance surface 101a are formed as annularsegments that are concentric with the optical axis as shown in FIG. 10.In FIGS. 9 and 10, the width of each annular segment and the differencein height between annular segments are shown enlarged to provide betterunderstanding.

The shift amount in the optical direction of adjacent annular zone t ofindividual planes is defined by the following condition:

    t=mλ.sub.0 /(n-1)

where m is an integer, n is the refractive index, and λ₀ is an arbitrarywavelength in the operating wavelength range.

As shown in FIG. 11, the optical pathlength of rays of light at thewavelength λ₀ is offset by mλ₀ as they pass through adjacent planes and,after emerging from the exit surface, they will form a plane wave again.

If the wavelength changes to λ₀ +Δλ, the wavefront is offset by aboutmΔλ between adjacent planes (ignoring the change that occurs in therefractive index of the constituent material of the chromatic aberrationcorrecting device on account of the change in wavelength) and theoptical pathlength difference will not be an integral multiple of thewavelength. Hence, the emerging wavefront is not a plane wave but agenerally spherical wave having power as shown in FIG. 12.

If the chromatic aberration correcting device 101 is of a shape thatresembles macroscopically a concavo-plane lens, it is capable ofcanceling the chromatic aberration that develops in an ordinaryrefractive using positive lens; hence, by using this device incombination with an objective lens for optical disk as shown in FIG. 13where the objective lens is indicated by 102, correction of chromaticaberration can be accomplished. Shown by 103 in FIG. 13 is an opticaldisk cover glass.

We then describe the effect of the chromatic aberration correctingdevice when it is positioned a certain distance away from the objectivelens.

Consider optical system in which two lens groups A and B are spaced by adistance of L. If parallel light enters this optical system, thedistance from the last lens surface to the imaging plane, which isgenerally called the back focus fB, is expressed by the followingequation (1A) in which φA and φB represent the powers of the respectivelens groups. By differentiating equation (1) with respect to φB, L andφA, we get equations (2A), (3A) and 4(A), respectively:

    fB=(1-φAL)/(φA+φB-φAφBL)               (1A)

    dfB/dφB=-(1-φAL).sup.2 /(φA+φB-φAφBL).sup.2(2A)

    dfB/dL=-φA.sup.2 /(φA+φB-φAφBL).sup.2  (3A)

    dfB/dφA=-1/(φA+φB-φAφBL).sup.2         (4A)

If the lens group A is assumed to be a chromatic aberration correctingdevice having no power, differential equations (2A), (3A) and (4A) canbe simplified as follows:

    dfB/dφB≈-1/φB.sup.2                        (5A)

    dfB/dL≈0                                           (6A)

    dfB/dφA≈-1/φB.sup.2                        (7A)

Hence, the following conclusion is reached: if lens group A has a veryweak power, a change in distance L will cause no change in the focusingposition; if the power of lens group B changes, there occurs a shift inthe focus position as represented by equation (5A); and if the power oflens group A changes, there occurs a change in the focus position asrepresented by equation (7A).

Thus, in order to insure that there will be no shift in the focusingposition even if a change in wavelength causes corresponding changes inthe powers of lens groups A and B, one may set the respective lensgroups so that the amount of change in the power of one lens group willcancel the amount of change in the power of the other lens group,namely, the coefficients of differentiation of the powers of therespective lens groups with respect to wavelength λ will satisfy therelationship expressed by the following equation (8A):

    dφA/dλ=-dφB/dλ                       (8A)

The change in the power of lens group B in response to the change inwavelength is expressed by equation (9A) in relation to the change inback focus. If lens group A is assumed to be a diffractive lens, itspower which is proportional to wavelength is expressed by the followingequation (10A):

    dφB/dλ=-(dfB/dλ)φB.sup.2             (9A)

    dφA/dλ=φA/λ                          (10A)

Substituting equations (9A) and (10A) into equation (8A), the power ofthe chromatic aberration correcting device which is composed as adiffractive lens is given by:

    φA=-(dfB/dλ)λφB.sup.2                (11A)

Take, for example, the case where lens group B is composed of anobjective lens that has a focal length of 3 mm, that is to handle lightfrom a laser operating at a wavelength of 780 nm and that hasdfB/dλ=0.060 μm/nm. The chromatic aberration correcting device may beset to have power φA that is expressed by:

    φA=0.06×10.sup.-3 ·780·(1/3).sup.2 =1/192.3(12A)

Thus, the chromatic aberration that occurs in the objective lens can becorrected by using a positive diffractive lens having the focal length192 mm. It should, however, be noted that in order to adjust the overallpower of the chromatic aberration correcting device to zero, a negativerefractive lens having a focal length of -192 mm must be positioned incontact with this diffractive lens. If the negative lens is composed ofa diffractive lens, dispersion will contribute a slight improvement inthe chromatic aberration correcting effect.

If the negative lens under discussion is made of BSL7 (trade name ofOhara Co., Ltd.; refractive index=1.51072 at wavelength λ₀ 780 nm), theresult is a concave-plane lens that has a spherical entrance surfacewith a curvature radius of -98.058 mm and a plane exit surface.

However, if the positive diffractive lens and the negative refractivelens are provided as separate members, the number of devices involvedcannot be reduced to realize a lower manufacturing cost. To this end,the positive diffractive lens is desirably combined with the negativerefractive lens into an integral unit.

To realize an integral unit, the concave surface of the negative lensmay be composed of step-like planes that are arranged in such a way thatthe axial pitch P will satisfy the equation: λ₀ /(n-1)=1.5273 μm. Thisdesign helps provide a chromatic aberration correcting device that iscapable of correcting chromatic aberration by working as a diffractivelens having the focal length 192 mm and which has no power at theoperating center wavelength 780 nm since the light of first-orderdiffraction will travel straight.

Assume a coordinate system that extends in the axial direction along thepath of travelling light; if the coordinate of the point at theintersection with the optical axis is assumed to be zero, the coordinateX(h) of the area that departs from the optical axis by distance h isexpressed by equation (13A) if the area is a curved plane and byequation (14A) if the area is composed of step-like planes: ##EQU5##where Int(x) is a function that gives the integral portion of x, and Cis any constant that satisfied 0≦C<1.

When using the chromatic aberration correcting device in combinationwith the aforementioned objective lens, the specific geometry of thedevice is as shown below in Table 9.

                  TABLE 9    ______________________________________    h (mm)       X (μm)      n: 1.51072    ______________________________________    0.000 ˜ 0.387                 0.00    ˜0.670 ˜1.53    ˜0.865 ˜3.05    ˜1.024 ˜4.58    ˜1.161 ˜6.11    ˜1.284 ˜7.64    ˜1.395 ˜9.16    ˜1.499 ˜10.69    ˜1.596 ˜12.22    ˜1.687 ˜13.75    ˜1.773 ˜15.27    ˜1.856 ˜16.80    ˜1.935 ˜18.33    ˜2.011 ˜19.85    ˜2.084 ˜21.38    ˜2.155 ˜22.91    ______________________________________

In the example described above, the axial pitch is adjusted to λ₀/(n-1); if the operating wavelength is within a narrow range, the axialpitch may be adjusted to mλ₀ /(n-1) (m: integer) and the light ofmth-order diffraction may safely be used without lowering thediffraction efficiency.

It should be particularly noted here that the peripheral portion of thechromatic aberration correcting device is usually characterized by thesmaller width of annular segments than those in the central portion.Hence, by gradually increasing the value of m starting from unity so asto give different pitches, one can prevent the width of annular segmentsin the peripheral portion from becoming unduly narrow. Equation (14A)may be modified as follows with m being taken into account: ##EQU6##

In the example described above, the chromatic aberration correctingdevice is composed in such a manner that its shape is macroscopicallylike a concave-plane lens, whereby it is capable of correcting thechromatic aberration that has developed in a convex lens. It should benoted that the device may be turned around to produce a plano-concavelens which will function in entirely the same manner as theconcave-plane lens. Alternatively, both sides of the chromaticaberration correcting device may be rendered to have macroscopicallycurved surfaces as shown in FIG. 14. The curved surface serving as areference is not limited to the spherical surface used in the exampleand it may be an aspheric surface.

Further, the chromatic aberration correcting device may be formed as amacroscopically convexo-plane lens of the type shown in FIG. 15 or as abiconvex lens of the type shown in FIG. 16; devices of these types canbe used to correct the chromatic aberration that has developed in thenegative refractive lens.

FIG. 17 shows optical system in a magnetooptical information recordingand reproducing apparatus that contains the chromatic aberrationcorrecting device described hereinabove. Divergent light issuing from alaser diode 10 serving as a light source is collimated by a collimatorlens 11 and thereafter shaped to have a circular cross section by meansof a beam shaping prism 12. The shaped laser beam is reflected by aprism 13 to pass through the chromatic aberration correcting device 101;the beam is thereafter reflected by a mirror 14 and focused by anobjective lens 102 to form a spot on disk D.

Both the objective lens 102 and the mirror 14 are mounted on a carriage15, which is slidable along guide rails 16 in the radial direction ofdisk D indicated by the two-head arrow in FIG. 17.

The reflected light from disk D makes the second passage throughobjective lens 102, mirror 14 and chromatic aberration correcting lens101 and is reflected by the prism 13; part of the reflected light passesthrough a condenser lens 17 to be collected on a light-receiving element18 for signal reproduction and the remainder passes through a condenserlens 19 to be collected on a light-receiving element 20 for error signaldetection. In accordance with the reflected light received, the element18 outputs the information recorded on the disk whereas the element 19outputs an error signal such as a tracking error or a focusing errorsignal.

A modification of the optical system described above is shown in FIG.18. In this modified example, the chromatic aberration correcting device101 is attached to the prism 13.

The laser diode 10 will produce an output which, in a recording mode,increases intermittently in a region where it changes the direction ofmagnetization on the disk and which is small and constant in areproduction mode. This change in power causes a corresponding change inoscillation wavelength. However, as described above, the chromaticaberration correcting device 101 is inserted between the light sourceand the objective lens in accordance with the present invention, wherebythe convergence of light beams can be varied slightly as there occurs achange in wavelength so as to suppress the undesired shift in theposition where the condenser lens 102 collects light beams.

As described on the foregoing pages, the present invention permits asingle optical element to correct the chromatic aberration that developsin a positive or a negative lens, thereby producing a lens system thatuses a smaller number of optical elements and which yet is free fromchromatic aberration. Therefore, the present invention will contributeto the manufacture of a lighter lens system at a lower cost.

If the chromatic aberration correcting device of the present inventionis used in optical system for an optical information recording andreproducing apparatus, the position where the condenser lens collectslight beams can be prevented from shifting on account of variations inthe wavelength of light source and this insures the apparatus to beoperated consistently even if the operating wavelength is switched fromone value to another.

The following embodiments relate to a device for correcting thechromatic aberration inherent in optical system. More particularly, thepresent invention relates to a chromatic aberration correcting devicethat is intended for use in combination with a single aspheric surfacethat is corrected for aberrations other than chromatic aberration.

The conventional chromatic aberration correcting device is positioned ina substantially afocal portion of optical system and, depending upon ofthe wavelength of incident parallel light, transforms it to eitherdivergent or convergent light so as to cancel the axial chromaticaberration that develops in an objective lens.

The lens to be corrected for chromatic aberration is typically apositive lens that is corrected for spherical aberration at a singlewavelength. The focal length of a positive lens decreases at shorterwavelengths and increases at longer wavelengths (assuming that the lensis used at wavelengths near visible light). Therefore, in order tocancel the axial chromatic aberration and prevent the shifting of focusposition, the rays of light entering the positive lens may betransformed to divergent light if the incident light has shortwavelength and to convergent light if it has long wavelength.

Optical system using this conventional chromatic aberration correctingdevice is capable of correcting axial chromatic aberration; however, itexperiences varying spherical aberrations in response to changes inwavelength and, hence, under those conditions which cause a wide rangeof changes in wavelength, it has been impossible for the optical systemto maintain good performance both at the wavelength before change and atthe wavelength after change.

Even if a positive lens is corrected for spherical aberration at areference wavelength, the spherical aberration is undercorrected withrespect to shorter-wavelength light that experiences a higher refractiveindex and it is overcorrected with respect to longer-wavelength lightthat experiences a lower refractive index. This is the change thatoccurs to spherical aberration depending upon wavelength.

If parallel light is transformed to either divergent or convergent lightunder the action of the conventional chromatic aberration correctingdevice, this transformation, which is equivalent to the change from anobject at infinity from a positive lens to an object at finite distance,will cause a change in spherical aberration. As a result of this change,the spherical aberration is undercorrected if divergent light enters thepositive lens and it is overcorrected if convergent light enters thepositive lens. This is the change that develops in spherical aberrationunder the action of the chromatic aberration correcting device.

The changes in spherical aberration due to these two factors take placein the same direction and, hence, it has been impossible to correct themby optical system that uses the conventional chromatic aberrationcorrecting device.

If the operating wavelength band is as narrow as the expected range ofchange in the oscillation wavelength of a laser diode, the change inspherical aberration is very small and causes no great problems.However, if the operating wavelength is expected to change over a widerrange as in the case where two light sources emitting at wavelengthsthat are not close to each other are selectively operated, asexemplified by the use of a near infrared laser diode (780 nm) and avisible red laser diode (680 nm) or the use of a He--Ne laser (633 nm)and the SHG wave from a YAG laser (532 nm), or if a plurality ofwavelengths are used simultaneously, a greater change in sphericalaberration is also expected and must be dealt with by some method.

The present invention has been accomplished under these circumstancesand has an object providing a chromatic aberration correcting devicethat not only corrects the axial chromatic aberration developing in apositive lens but which also is capable of suppressing the change inspherical aberration even if it is used on two light sources that emitlight beams at wavelengths that are not close to each other and whichare selectively operated at those wavelengths.

EXAMPLES

Several examples of the chromatic aberration correcting device accordingto the present invention are described below.

In order to insure that both the change in spherical aberration thatdevelops in a positive lens depending upon wavelength and the sphericalaberration that occurs in response to the incidence of divergent orconvergent light on the positive lens are corrected by the chromaticaberration correcting device, the surface of the device that has achromatic aberration correcting action need be adjusted have to ageometry that generates spherical aberration. Hence, the chromaticaberration correcting device of the present invention is so adapted thatit generates a divergent wavefront having an overcorrected sphericalaberration in response to the incidence of parallel beams of light at awavelength shorter than a reference wavelength and that it generates aconcentrating wavefront having an undercorrected spherical aberration inresponse to the incidence of parallel beams of light at a wavelengthlonger than the reference wavelength.

The chromatic aberration correcting device is available in two specifictypes: a refractive type that is composed by cementing a positive and anegative lens that are formed of materials having substantially nodifference in refractive index but having different dispersion values atthe reference wavelength; and a diffraction type that has annularsegments formed in steps on either a light entrance surface or a lightexit surface or both, the annular segments being composed of planesperpendicular to and concentric with the optical axis. Theabove-described spherical aberration can be generated by insuring thatthe cemented surface (in the case of a refractive type) or the basecurve which is a macroscopic curvature of the radius of curvature of theplanes formed in steps (in the case of diffraction type) is an asphericsurface the radius of curvature of which decreases in absolute valuewith the increasing distance from the optical axis.

Lower-order spherical aberrations can generally be expressed by abiquadratic function of the height of ray incidence; therefore, most ofthe changes in spherical aberration can be effectively corrected byproviding the chromatic aberration correcting device with a surfacehaving fourth-order asphericity. It should, however, be noted that if asingle aspheric lens is to be used as the positive lens to be corrected,the aspheric surface of the chromatic aberration correcting device ispreferably designed as an aspheric surface that resembles a spheroidalsurface having a positive conic constant and this enables more effectivecorrection in that it can handle the component of a change inhigher-order aberrations.

When the departure ε(h) from the spheroidal surface at a point havingdistance h from the optical axis is expressed by the following equation(1B), the aspheric surface of interest which resembles the spheroidalsurface desirably satisfies the following condition (2B) (in the case ofa refractive type) or (4B) (in the case of a diffraction type) at allvalues of distance h within the effective maximum radius of passingbeams of light: ##EQU7## where ΔX(h) is the sag of the aspheric surface;C is the paraxial curvature; K is the conic constant; λ is the maximumoperating wavelength; and ΔnMAX is the absolute value of difference inrefractive index in the case where the difference between the refractiveindices of the media on both sides of the cemented surface is thegreatest in the operating wavelength band; and n is the refractiveindex.

In the case of a diffraction-type chromatic aberration correctingdevice, when the axial displacement of the base curve at a point havingdistance h from the optical axis is written as ΔX(h), the displacementΔX'(h) of the planes formed in steps at a point having distance h fromthe optical axis is given by the following equation (3B):

    ΔX'(h)=(mλ.sub.0 /(n-1))Int((ΔX(h)/(mλ.sub.0 /(n-1)))+0.5)                                             (3B)

where m is an integer; n is the refractive index; λ₀ is the wavelengthat which the chromatic aberration correcting device is used or anarbitrary wavelength within the operating wavelength range of thedevice; and Int(x) is a function giving an integer not greater then x.

Condition (2B) must be satisfied in order to produce an opticalpathlength difference of 1λ or less when a chromatic aberrationcorrecting device of a refractive type is used. Similarly, condition(4B) must be satisfied in order to produce an optical pathlengthdifference of 1λ or less when a chromatic aberration correcting deviceof a diffraction type is used. If these conditions are not met, the rms(root mean square) value of wavefront aberrations will exceed 0.1λ andthe device is no longer suitable for use in the recording orreproduction of optical information.

FIG. 19 is a simplified diagram showing schematically a positiveobjective lens to be corrected by the chromatic aberration correctingdevices used in Examples 1B to 3B that follow. The specific numericaldata for this lens are listed in Table 1B, in which NA denotes thenumerical aperture, f the focal length, ω the half view angle, fb theback focus, r the radius of curvature, d the lens thickness or theaerial distance between adjacent lenses, ni the refractive index atwavelength i nm, and θ the Abbe number. The first and second surfaces inFIG. 19 define the objective lens having an aspheric surface on bothsides, and the third and fourth surfaces define the cover glass of anoptical disk.

The aspheric surface is expressed by the following equation: ##EQU8##where x is the distance by which the coordinates at the point on theaspheric surface where the height from the optical axis is Y aredeparted from the plane tangent to the vertex of the aspheric surface; Cis the curvature (1/r) of the vertex of the aspheric surface; K is theconic constant; and A4, A6, A8 and A10 are the aspheric coefficients ofthe fourth, sixth, eighth and tenth orders, respectively.

The conic constants and aspheric coefficients for the first and secondsurfaces are listed in Table 2B. FIG. 20 shows the spherical aberrationSA, sine condition SC, and the chromatic aberration that is expressed interms of spherical aberrations at wavelengths of 780 nm and 680 nm.

                  TABLE 1B    ______________________________________    NA = 0.55 f = 3.00 ω = 1.4° fb = 1.088    Surface    No.   r       d       n588   ν  n780   n680    ______________________________________    1     1.894   2.200   1.49700                                 81.6  1.49282                                              1.49461    2     -4.186  1.088    3     ∞ 1.200   1.58547                                 29.9  1.57346                                              1.57834    4     ∞    ______________________________________

                  TABLE 2B    ______________________________________    1st surface     2nd surface    ______________________________________    K =      -0.5800       K =       0.000    A4 =       0.7540 × 10.sup.-3                           A4 =      0.3250 × 10.sup.-1    A6 =     -0.3670 × 10.sup.-4                           A6 =    -0.1000 × 10.sup.-1    A8 =       0.2800 × 10.sup.-4                           A8 =      0.2000 × 10.sup.-2    A10 =    -0.3600 × 10.sup.-4                           A10 =   -0.1820 × 10.sup.-3    ______________________________________

EXAMPLE 1B

FIG. 21 shows optical system in which the refractive-type chromaticaberration correcting device according to Example 1B of the presentinvention is combined with the objective lens shown in FIG. 19. Thecemented surface r2 of the correcting device is ellipsoidal and ε(h) iszero within the effective radius. The specific numerical data for theoptical system are listed in Table 3B. The first to third surfacesdefine the chromatic aberration correcting device, the fourth and fifthsurfaces define the objective lens, and the sixth and seventh surfacesdefine the cover glass of an optical disk. In Example 1B, the second,fourth and fifth surfaces are aspheric and the associated asphericcoefficients are listed in Table 4B. FIG. 22 shows the aspheric andchromatic aberrations that develop in the optical system composed inaccordance with the data listed in Table 3B.

                  TABLE 3B    ______________________________________    FNO-1:0.9 f = 3.00 ω = 1.4° fb = 0.00    Surface    No.   r       d       n588   ν  n780   n680    ______________________________________    1     ∞ 2.000   1.75500                                 52.3  1.74523                                              1.74940    2     -4.400  1.000   1.76182                                 26.5  1.74404                                              1.75132    3     ∞ any distance    4       1.894 2.200   1.49700                                 81.6  1.49282                                              1.49461    5     -4.186  1.088    6     ∞ 1.200   1.58547                                 29.9  1.57346                                              1.57834    7     ∞    ______________________________________

                  TABLE 4B    ______________________________________    4th surface  5th surface    2nd surface    ______________________________________    K =   -0.5800    K =       0.0000 K =  0.2500 × 10    A4 =    0.7540 × 10.sup.-3                     A4 =      0.3250 × 10.sup.-1    A6 =  -0.3670 × 10.sup.-4                     A6 =    -0.1000 × 10.sup.-1    A8 =    0.2800 × 10.sup.-4                     A8 =      0.2000 × 10.sup.-2    A10 = -0.3600 × 10.sup.-4                     A10 =   -0.1820 × 10.sup.-3    ______________________________________

FIG. 23 shows optical system that has the same configuration as inExample 1B except that the cemented surface r2 is spherical. FIG. 24shows the spheric and chromatic aberrations that develop in the opticalsystem shown in FIG. 23. Comparing FIGS. 22 and 24, one can see that theamount of change in spherical aberration due to variations in wavelengthis reduced if the geometry of the cemented surface is changed fromspherical to ellipsoidal.

EXAMPLE 2B

FIG. 25 shows optical system in which a chromatic aberration correctingdevice of a diffraction type is combined with the objective lens shownin FIG. 19. As shown in FIGS. 26A and 26B, a diffraction-type chromaticaberration correcting device has annular segments formed in steps asthey are perpendicular to and concentric with the optical axis.

Table 5B lists numerical data for the optical system in which thediffraction-type chromatic aberration correcting device of Example 2B iscombined with the objective lens shown in FIG. 19. The correcting deviceis such that the base curve which is a macroscopic curvature of surfacer1 formed in steps provides a fourth-order aspheric surface. FIG. 27shows the spherical and chromatic aberrations that develop in theoptical system composed in accordance with the data shown in Table 5B.

In Example 2B, the first, third and fourth surfaces are aspheric and theassociated aspheric coefficients are listed in Table 6B.

                  TABLE 5B    ______________________________________    FNO-1:0.9 f = 3.00 ω = 1.4° fb = 0.00    Surface    No.   r        d       n588   ν n780   n680    ______________________________________    1     -104.400 1.000   1.51633                                  64.1 1.51072                                              1.51315    2     ∞  any distance    3     1.894    2.200   1.49700                                  81.6 1.49282                                              1.49461    4     -4.186   1.090    5     ∞  1.200   1.58547                                  29.9 1.57346                                              1.57834    6     ∞    ______________________________________

                  TABLE 6B    ______________________________________    3rd surface 4th surface   1st surface    ______________________________________     K = -0.5800                 K =   0.0000  K =   0.0000     A4 =   0.7540 × 10.sup.-3                 A4 =   0.3250 × 10.sup.-1                              A4 = -0.3400 × 10.sup.-3     A6 = -0.3670 × 10.sup.-4                 A6 = -0.1000 × 10.sup.-1     A8 =   0.2800 × 10.sup.-4                 A8 =   0.2000 × 10.sup.-2    A10 = -0.3600 × 10.sup.-4                A10 = -0.1820 × 10.sup.-3    ______________________________________

EXAMPLE 3B

Table 7B lists numerical data for optical system in which the chromaticaberration correcting device of Example 3B is combined with theobjective lens shown in FIG. 19. The correcting device is such that thebase curve which is a macroscopic curvature of surface r1 formed insteps provides an ellipsoidal surface and ε(h) is zero within theeffective radius. FIG. 28 shows the spherical and chromatic aberrationsthat develop in the optical system composed in accordance with the datalisted in Table 7B. In Example 3B, the first, third and fourth surfacesare aspheric and the associated coefficients are listed in Table 8B.

                  TABLE 7B    ______________________________________    FNO-1:0.9 f = 3.00 ω = 1.4° fb = 0.00    Surface    No.   r        d       n588   ν n780   n680    ______________________________________    1     -104.400 1.000   1.51633                                  64.1 1.51072                                              1.51315    2     ∞  any distance    3     1.894    2.200   1.49700                                  81.6 1.49282                                              1.49461    4     -4.186    5     ∞  1.200   1.58547                                  29.9 1.57346                                              1.57834    6     ∞    ______________________________________

                  TABLE 8B    ______________________________________    3rd surface 4th surface    1st surface    ______________________________________     K = -0.5800                 K =   0.0000  K = 0.2000 × 10.sup.-4     A4 =   0.7540 × 10.sup.-3                 A4 =   0.3250 × 10.sup.-1     A6 = -0.3670 × 10.sup.-4                 A6 = -0.1000 × 10.sup.-1     A8 =   0.2800 × 10.sup.-4                 A8 =   0.2000 × 10.sup.-2    A10 = -0.3600 × 10.sup.-4                A10 = -0.1820 × 10.sup.-3    ______________________________________

FIG. 29 shows the spherical and chromatic aberrations that develop inoptical system that has the same configuration as in Examples 2B and 3Bexcept that the base curve for the surface formed in steps provides aspherical y surface. Comparing FIGS. 27 and 28, one can see that theamount of change in spherical aberration due to variations in wavelengthis reduced if the geometry of the base curve provides either afourth-order aspheric or an ellipsoidal surface rather than a sphericalsurface.

FIG. 30 is a simplified diagram showing schematically the singlepositive lens having an aspheric surface on both sides that is to becorrected by the chromatic aberration correcting devices according toExamples 4B and 5B. The specific numerical data for this lens are listedin Tables 9B and 10B. The spherical aberration that develops in thislens alone, as well as the chromatic aberration that is expressed interms of spherical aberrations at wavelengths of 633 nm and 532 nm areshown in FIG. 31.

                  TABLE 9B    ______________________________________    NA = 0.55 f = 3.29 ω = 1.7° fb = 1.332    Surface    No.     r         d      n588    ν n633    ______________________________________    1         2.180   2.250  1.54358 55.6 1.54151    2       -6.250    1.332    3       ∞   1.200  1.58547 29.9 1.58156    4       ∞    ______________________________________

                  TABLE 10B    ______________________________________    1st surface     2nd surface    ______________________________________    K =      -0.3265       K =       0.0000    A4 =     -0.2265 × 10.sup.-2                           A4 =      0.1670 × 10.sup.-1    A6 =     -0.5014 × 10.sup.-3                           A6 =    -0.5080 × 10.sup.-2    A8 =     -0.7162.10.sup.-5                           A8 =      0.8000 × 10.sup.-3    A10 =    -0.3194 × 10.sup.-4                           A10 =   -0.4848 × 10.sup.-4    ______________________________________

EXAMPLE 4B

FIG. 32 is a simplified diagram showing schematically optical system inwhich the refractive-type chromatic aberration correcting deviceaccording to Example 4B of the present invention is combined with theobjective lens shown in FIG. 30. The specific numerical data for theoptical system are listed in Tables 11B and 12B. The cemented surface r2of the correcting device is ellipsoidal and ε(h) is zero within theeffective radius. FIG. 33 shows the spherical and chromatic aberrationsthat develop in the optical system composed in accordance with the datalisted in Tables 11B and 12B.

                  TABLE 11B    ______________________________________    FNO = 1:0.9 f = 3.29 ω = 1.7° fb = 0.00    Surface    No.   r       d       n588   ν  n633   n532    ______________________________________    1     ∞ 0.800   1.74077                                 27.8  1.73541                                              1.74959    2     2.280   2.000   1.74100                                 52.7  1.73804                                              1.74567    3     ∞ any distance    4     2.180   2.250   1.54358                                 55.6  1.54151                                              1.54680    5     -6.250  1.332    6     ∞ 1.200   1.58547                                 29.9  1.58156                                              1.59194    7     ∞    ______________________________________

                  TABLE 12B    ______________________________________    4th surface   5th surface     2nd surface    ______________________________________    K =    -0.3265    K =        0.0000 K = 0.6000    A4 =   -0.2263 × 10.sup.-2                      A4 =       0.1670 × 10.sup.-1    A6 =   -0.5014 × 10.sup.-3                      A6 =     -0.5080 × 10.sup.-2    A8 =   -0.7162 × 10.sup.-5                      A8 =       0.8000 × 10.sup.-3    A10 =  -0.3194 × 10.sup.-4                      A10 =    -0.4848 × 10.sup.-4    ______________________________________

FIG. 34 shows optical system having the same configuration as describedabove except that the cemented surface r2 of the chromatic aberrationcorrecting device is spherical, and FIG. 35 shows the spherical andchromatic aberrations that develop in the optical system underconsideration. Obviously, the use of an ellipsoidal cemented surface iseffective not only in bringing the profiles of spherical aberrationcurves close to each other at the two wavelengths but also in reducingthe overall amount of spherical aberrations.

EXAMPLE 5B

FIG. 36 in a simplified diagram showing schematically optical system inwhich the diffraction-type chromatic aberration correcting deviceaccording to Example 5B of the present invention is combined with theobjective lens shown in FIG. 30. The specific numerical data for theoptical system are listed in Tables 13b and 14B. In the correctingdevice of Example 5B, the base curve for the planes formed in steps isellipsoidal and ε(h) is zero within the effective radius. The sphericaland chromatic aberrations that develop in the optical system composed inaccordance with the data listed in Tables 13B and 14B shown in FIG. 37.

                  TABLE 13B    ______________________________________    f = 3.29 ω = 1.7° fb = 0.00    Surface    No.   r       d       n588   ν  n633   n532    ______________________________________    1     ∞ 2.000   1.51633                                 64.1  1.51462                                              1.51900    2     41.000  any distance    3      2.180  2.250   1.54358                                 55.6  1.54151                                              1.54680    4     -6.250  1.341    5     ∞ 1.200   1.58547                                 29.9  1.58156                                              1.59194    6     ∞    ______________________________________

                  TABLE 14B    ______________________________________    3rd surface  4th surface    1st surface    ______________________________________    K =   -0.3265    K =     0.0000   K = 0.2450 × 10.sup.+3    A4 =  -0.2263 × 10.sup.-2                     A4 =    0.1670 × 10.sup.-1    A6 =  -0.5014 × 10.sup.-3                     A6 =    -0.5080 × 10.sup.-2    A8 =  -0.7162 × 10.sup.-5                     A8 =    0.8000 × 10.sup.-3    A10 = -0.3194 × 10.sup.-4                     A10 =   -0.4848 × 10.sup.-4    ______________________________________

FIG. 38 shows the spherical and chromatic aberrations that develop inoptical system having the same configuration as in Example 5B exceptthat the base curve for the planes formed in steps in the chromaticaberration correcting device is spherical. Comparing FIGS. 37 and 38,one can see that the variation in spherical aberration is reduced if thebase curve is made ellipsoidal.

As described on the foregoing pages, the present invention not onlycorrects the axial chromatic aberration that develops in a condenserlens on account of variations in wavelength but it also is capable ofsuppressing the variations in spherical aberration. Hence, it has theadvantage of expanding the range over which the fluctuation in theperformance of optical system due to variations in wavelength can besuppressed.

Because of these advantages, the present invention offers a practicalbenefit in that even a lens that is yet to be corrected for chromaticaberration can be used on an optical information recording apparatusthat employs two wavelengths fairly remote from each other or on aninformation reading apparatus that employs a light-emitting diode and awhite light source, and this helps realize a compact unit of opticalsystem.

The following embodiments relate to optical system for an opticalinformation recording and reproducing apparatus which records orreproduces information on a medium such as an optical disk. Theembodiments of the present invention also relate to a chromaticaberration correcting device that is to be installed in the opticalsystem.

The present invention has been accomplished under these circumstancesand has as an object providing optical system for an optical informationrecording and reproducing apparatus that is effectively corrected forchromatic aberration without using more optical elements than in thecase where chromatic aberration is not corrected. Another object of thepresent invention is to provide a chromatic aberration correcting devicethat is to be used in the optical system.

Examples of the optical system for optical information recording andreproducing apparatus according to the present invention, as well as thechromatic aberration correcting device of the same invention aredescribed below.

EXAMPLE 1C

FIG. 39 shows the optical system for optical information recording andreproducing apparatus according to Example 1C of the present invention.Divergent light issuing from a laser diode 110 serving as a light sourceis collimated by a collimator lens 120; the collimated light then passesthrough a beam splitter 130 and is focused by an objective lens 140 toform a spot on an optical disk 150. The reflected light from the opticaldisk 150 makes reentry into the beam splitter 130 and part of it isreflected and passes through a condenser lens 160 to be collected by alight-receiving element 170. Depending upon the reflected light itreceives, the element 170 outputs either the information recorded on theoptical disk or a signal such as a tracking error or focusing errorsignal.

The beam splitter 130 is composed of two prisms 131 and 132 joinedtogether by a beam splitting surface 130a, and a concavo-plane lens 133that is cemented to prism 132 which faces the objective lens 140. Prism132 and lens 133 are typically made of two materials that havesubstantially the same refractive index but which have different Abbenumbers as shown in Table 1C below. This arrangement offers theadvantage that the cemented surface which is substantially powerless iscapable of generating chromatic aberration that is at least sufficientto cancel the chromatic aberration that develops in objective lens 140.

                  TABLE 1C    ______________________________________             Material                   nA'         nd      νd    ______________________________________    Prism 132  YGH51   1.74566     1.75500                                         52.33    Lens 133   TIH14   1.74475     1.76182                                         26.55    ______________________________________

(Names under "Material" are trade names of Ohara Co., Ltd.)

If desired, a concave surface may be formed on the side facing theprisms using a high-dispersion material whereas a plano-convex lens maybe formed of a low dispersion material. This arrangement also producesequally good chromatic aberration correcting effects.

Whichever arrangement is adopted, the only difference from the casewhere chromatic aberration is not corrected is that the shape of beamsplitter 130 is modified; hence, optical system that is effectivelycorrected for chromatic aberration can be offered without using anyadditional elements.

In Example 1C, one surface of prism 132 is made convex. If desired, thissurface may be rendered planar and a plano-convex lens may be combinedwith a convexo-plane lens to constitute a chromatic aberrationcorrecting device, which is attached to the beam splitter 130.

FIG. 40 shows a modification of Example 1C. In this modified example,laser light issues from laser diode 110 in a direction parallel to thesurface of optical disk 150; it then passes through collimator lens 120and beam splitter 130. A mirror 190 serving as an optical pathdeflecting means reflects the laser light toward the optical disk 150and the reflected light is focused by objective lens 140 to form a spoton the optical disk 150. As shown, the beam splitter 130 is composed ofprisms 131 and 132', as well as a convexo-plane lens 133'.

EXAMPLE 2C

FIG. 41 shows the optical system for optical information recording andreproducing apparatus according to Example 2C of the present invention.In this example, beam splitter 130 is composed of two prisms 131 and 134joined together by the beam splitting surface 130a, and planesperpendicular to the optical axis are formed in steps on one beampassing surface 134a of prism 134 as annular segments concentric withthe optical axis in such a way that they produce a macroscopicallyconcave shape.

The axial pitch P of annular planes is expressed by the followingequation:

    P=λ/(n-1)

where n is the refractive index of prism 134 and λ is the referencewavelength at which there is no change in wavefront, or at which nochromatic aberration will develop.

The surface 134a on which annular planes are formed in steps works as adiffraction grating; if incident light has a wavelength equal to thereference wavelength, the surface 134a will transmit the incident lightwithout causing any change in the wavefront but if the wavelength of theincident light is different from the reference wavelength, the surfacewill generate a predetermined chromatic aberration that is sufficient tocancel the chromatic aberration that develops in the objective lens 140.

EXAMPLE 3C

FIGS. 42 and 43 show the optical system for optical informationrecording and reproducing apparatus according to Example 3C of thepresent invention. In this example, beams of light issuing from laserdiode 110 pass through collimator lens 120 and the resulting parallellight passes through a beam splitter 180 that has a beam shapingcapability. The light is then reflected by mirror 190 and is focused byobjective lens 140 to form a spot on optical disk 150.

The beam splitter 180 is composed of two prisms 181 and 182 joinedtogether by a beam splitting surface 180a, and a convexo-plane lens 183cemented to the prism 182. The prisms and the lens are formed of thematerials listed in Table 2C below.

                  TABLE 2C    ______________________________________             Material                   nA'         nd      vd    ______________________________________    Prism 181  LAM54   1.74688     1.75700                                         47.82    Prism 182  TIH14   1.74475     1.76182                                         26.5    Lens 183   YGH51   1.74566     1.75500                                         52.33    ______________________________________

Since prisms 181 and 182 are made of two materials that havesubstantially the same refractive index but which have differentdispersion values, the bend in the optical path across the cementedsurface 180a is small and the desired beam shaping and chromaticaberration correcting effects can be exhibited without unduly increasingthe size of beam splitter 180.

As in the case shown in FIG. 39, the beams of light that has beenisolated by the beam splitter 180 from the light reflected from theoptical disk 150 pass through a condenser lens (not shown) to becollected on the light-receiving element 170.

EXAMPLE 4C

FIG. 44 shows the optical system for optical information recording andreproducing apparatus according to Example 4C of the present invention.Beams of light issuing from laser diode 110 pass through collimator lens120 and beam splitter 130. The light emerging from the beam splitter 130enters an optical path deflector 190 which deflects the light towardsoptical disk 150. In Example 4C, the optical path deflector 190 isadapted to have a chromatic aberration correcting action.

The optical path deflector 190 is composed of two prisms 191 and 192joined, together by a mirror surface 191a, as well as a concavo-planelens 193 cemented to the prism 192. Prism 192 and lens 193 are made oftwo materials that have substantially the same refractive index butwhich have different dispersion values, and this arrangement enables thedeflector 190 to correct the chromatic aberration that develops in theobjective lens 140. In this example, the optical path deflector 190 isso positioned that the chromatic aberration correcting surface faces theobjective lens; if desired, the deflector 190 may be reversed so thatthe chromatic aberration correcting surface will be positioned closer tothe collimator lens.

The light reflected from the optical disk 150 is then reflected by thebeam splitter 130 and passes through a condenser lens (not shown) to becollected on the light-receiving element.

EXAMPLE 5C

FIG. 45 shows the optical system for optical information recording andreproducing apparatus according to Example 5C of the present invention.In this example, a prism 194 is provided as an optical path deflectingmember and annular planes concentric with the optical axis are formed insteps on the light-transmitting surface 194a in such a way that thoseannular planes will produce a macroscopically concave shape, and thosestep-like planes on the surface 194a exhibit the ability to correct thechromatic aberration that develops in the objective lens 140.

The pitch of the annular planes and the function of thelight-transmitting surface 194a are the same as described in Example 2C.In the actual system, a beam splitter, a condenser lens and alight-receiving element are provided between the collimator lens 120 andthe prism 194 but they are not shown in FIG. 45.

As in Example 4C, the prism 194 may be so positioned that the surfacehaving step-like planes faces either the objective lens or thecollimator lens.

As described on the foregoing pages, the present invention depends on abeam splitter or an optical path deflector to provide a chromaticaberration correcting action and this helps provide improved opticalsystem that is effectively corrected for chromatic aberration withoutincreasing the number of elements that compose the optical system.

According to still another aspect, the present invention relates to thecorrection of chromatic aberration in a lens, more particularly, to ahybrid lens that uses a diffraction element to correct the chromaticaberration that develops in a single lens.

The degree of chromatic aberration that develops in a lens is determinedby the characteristics, in particular, the dispersion value, of theconstituent material of that lens. In the presence of dispersion, thepower of a lens varies with wavelength and, hence, the chromaticaberration that develops in a single lens cannot be effectivelycorrected by itself. Therefore, when designing optical system thatrequires the correction of chromatic aberration, the common practice isto combine two or more lens elements so that the lens powers whichdiffer with wavelength on account of dispersion cancel each other toaccomplish the intended correction of chromatic aberration.

A different approach was proposed in "Applications of DiffractiveOptical system", SPIE Vol. 1354, International Lens Design Conference(1990). According to this technique, annular planes that are concentricwith the optical axis are formed in steps on one surface of a glass lensto provide a diffractive action so that it is used to correct thechromatic aberration that develops in the glass lens. Annular planes maybe formed in steps on the surface of glass lens by etching but thismethod of working is not suitable for large-scale production and must bereplaced by a glass molding technique. Theoretically, this technique iscapable of producing single glass lenses that are corrected forchromatic aberration.

In practice, however, glass is so viscous that a structure as fine asthe diffraction surface cannot be exactly transferred from the mold tothe glass. If the diffraction surface cannot be transferred correctlyand if portions that should have differences in height come out smooth,light other than the diffracted light of the desired order will leakout; therefore, if the molded lens is used on an optical informationrecording and reproducing apparatus, the diameter of a beam spot formedon the medium will increases to such an extent that the bit error ratein the writing or reading of optical information will increase. If thelens is used as a photographic lens, the flare will increase or theresolution will decrease.

Compared to glass lenses, plastic lenses have the advantage that a finestructure can be easily transferred from the mold; therefore, plasticlenses are suitable for the making of a diffraction element. However,there is high likelihood that plastic lenses already become nonuniformin refractive index in the molding process; furthermore, the performanceof plastic lenses is apt to vary with the humidity of a use environmentor in response to the change in humidity.

If a plastic lens whose refractive index is not uniform in its interioris used as a focusing lens, the spot diameter will increase. If thatplastic lens is used as a large-aperture lens like photographic lens,marked image deterioration will take place. Therefore, plastic lenseshaving uneven index distribution are not suitable for use in eitherapplication.

The present invention has been accomplished under these circumstancesand has as an object providing a chromatic-aberration corrected hybridlens to which the pattern of a diffraction element can be transferredprecisely and which will not experience uneven distribution of internalrefractive indices even in the presence of environmental changes, etc.,thereby exhibiting consistent lens performance.

Examples of the hybrid lens according to the present invention aredescribed below with reference to the accompanying drawings. As shownschematically in FIG. 46A, the hybrid lens of the examples comprises aglass lens 201 having a refractive action and a plastic diffractionelement 202 that is joined to one surface of the glass lens 201.

Depending on the type of diffraction, diffraction elements are availableeither as an amplitude type or as a phase type, the latter being dividedinto an index modulation type and a relief type. In the examples, aphase- and a relief-type diffraction element is used in view of the highutilization of light and the ease of manufacture.

As shown in FIG. 46B, the side of the phase- and relief-type diffractionelement 202 that is not joined to the glass lens 201 is provided with aplurality of annular surfaces 203 that are concentric with the opticalaxis Ax and which are formed in steps in such a way that the lensthickness increases as a function of the distance from the optical axisAx.

An optical pathlength difference occurs between light that passesthrough a medium having a thickness of t and light that passes throughair, and this pathlength difference is given by (n-1)t, with n being therefractive index of the medium. Therefore, the axial difference in thethickness of the diffraction element 202 between adjacent annularsegments must be equal to t that is given by the following equation(1D), or an integral multiple of t:

    t(h)=λ/(n-1)                                        (1D)

where λ is the operating wavelength.

Furthermore, the ratio between t(n-1), or the optical pathlengthdifference due to t(i.e., the axial difference in the thickness of thediffraction element between individual annular segments), and wavelengthλ₀ desirably satisfies the following condition (A):

    0.8≦t(n-1)/λ.sub.0 ≦10                (A)

If the hybrid lens of the examples is to be used as a bright (high NA)lens such as one that is to be used on an optical information recordingand reproducing apparatus or in the case where the lens is to be used asa wide-angle lens, the ratio between t(n-1) and λ₀ desirably satisfiesthe following condition (2D):

    0.8≦t(n-1)/λ.sub.0 ≦1.0               (2D)

Suppose here that t(n-1)/λ₀ is unity. If a lens that uses a laser diodeas a light source that operates at varying wavelengths with thereference value (λ₀) lying at 780 nm is to be manufactured from LAL 13(trade name of Ohara Co., Ltd.; n780=1.68468), the axial difference (t)in the thickness of the diffraction element between individual annularsurfaces is calculated as follows:

    t=0.780×10.sup.-3 /(n-1)=0.780×10.sup.-3 /0.68468=1.14×10.sup.-3                             (3D)

The 1.14 μm difference in thickness is so fine that it is impossible forthe glass molding technique to have the pattern of the mold transferredprecisely to the highly viscous glass. It is for solving this problemthat the plastic diffraction element 202 is used in the presentinvention.

EXAMPLE 1D

FIG. 47 shows optical system that uses the hybrid lens according toExample 1D of the present invention, in which the hybrid lens is used asan objective lens in an optical disk system. Beams of parallel lightentering the optical system from the left are focused by the objectivelens composed of glass lens 201 and diffraction element 202, so as toform a spot on the recording surface located on the inner (right) sideof the cover glass of the optical disk D.

The surface that is on the left side, or the side the closest to theobject, is a discontinuous surface on which annular segments are formedand which serves as a diffracting surface. The base curve which is amacroscopic shape of that discontinuous surface is aspheric. Glass lens201 has a spherical surface on both sides.

The specific numerical data for Example 1D are listed in Table 1D, inwhich symbol λ₀ denotes the operating wavelength, f the focal length, NAthe numerical aperture, r the radius of curvature, d the lens thicknessor the aerial distance between individual lenses, and the refractiveindex at the d-line, vd the Abbe number, and n780 the refractive indexat the wavelength 780 nm. FIG. 48 shows the two aberrations that developin the system composed in accordance with the data listed in Table 1D:chromatic aberration expressed in terms of spherical aberrations at 770nm, 780 nm and 790 nm, as well as astigmatism (S, sagittal; M,meridional).

                  TABLE D1    ______________________________________    λ.sub.0 = 780 nm f = 3.30 mm NA = 0.55    Surface    No.     r           d      nd      νd                                            n780    ______________________________________    1       Diffracting 0.40                1.51653            surface    2        2.900      2.110  1.89799 34.0 1.88115    3       42.460      1.339    4       ∞     1.200  1.58547 29.9 1.57346    5       ∞    ______________________________________

The shape of the first surface of the hybrid lens is given by thecoefficients listed in Table 2D (see below) if the sag X(h) of theaspheric surface at the point that is departed from the optical axis bydistance h is defined by the following equation (4D) which has the termΔN added to the common expression of aspheric surface. Symbol N denotesthe number for the annular segment to which the point at height hbelongs, and each of the coefficients that define the aspheric surfaceis a function of N. Symbol INT(x) denotes a function for separating outthe integral part of x: ##EQU9## where r is the radius of curvature ofthe vertex of the aspheric surface; K is the conic constant; and A4, A6,A8 and A10 are the aspheric coefficients of the fourth, sixth, eighthand tenth orders, respectively.

                  TABLE 2D    ______________________________________           N =   INT(7.20 × h.sup.2 + 0.33 × h.sup.4 + 0.5)           rN =  2.700 + 5.13 × 10.sup.-4 × N           KN =  -0.5000           A4N = -1.570 × 10.sup.-3 + 1.00 × 10.sup.-6 × N           A6N = -1.900 × 10.sup.-4 + 3.02 × 10.sup.-7 × N           A8N = -1.900 × 10.sup.-5 + 1.51 × 10.sup.-8 × N           A10N =                 -9.000 × 10.sup.-7           ΔN =                 -0.001510 × N    ______________________________________

In the case where an objective lens is manufactured from a high-indexglass, lens performance satisfactory as a high-NA objective lens can beachieved without using an aspheric surface and, therefore, a sphericallens can effectively be used as in Example 1D discussed above.

EXAMPLE 2D

FIG. 49 shows optical system that uses the hybrid lens according toExample 2D of the present invention. In this example, too, the hybridlens is used as an objective lens in an optical disk system. Thespecific numerical data for Example 2D are listed in Table 3D. The firstsurface of the hybrid lens under consideration is a diffraction surfacewhereas the third surface is an ordinary smooth aspheric surface. FIG.50 shows the aberrations that develop in the system composed inaccordance with the data listed in Table 3D.

                  TABLE 3D    ______________________________________    λ.sub.0 = 780 nm f = 3.30 mm NA = 0.55    Surface    No.     r           d      nd      νd                                            n780    ______________________________________    1       Diffracting 0.040               1.51653            surface    2       2.400       2.110  1.58913 61.2 1.58252    3       Aspheric    1.355            surface    4       ∞     1.200  1.58547 29.9 1.57346    ______________________________________

The shape of the first surface is given by the coefficients listed inTable 4D (see below) if the sag X(h) of the aspheric surface at thepoint that is departed from the optical axis by distance h is defined bythe aforementioned equation (4D).

                  TABLE 4D    ______________________________________           N =   INT(4.41 × h.sup.2 + 0.20 × h.sup.4 + 0.5)           rN =  2.182 + 5.14 × 10.sup.-4 × N           KN =  -0.3610           A4N = -1.731 × 10.sup.-3 + 1.27 × 10.sup.-6 × N           A6N = -2.010 × 10.sup.-4 + 4.23 × 10.sup.-7 × N           A8N = -3.170 × 10.sup.-5 - 6.04 × 10.sup.-9 × N           A10N =                 6.000 × 10.sup.-7 + 6.04 × 10.sup.-9 × N           ΔN =                 -0.001510 × N    ______________________________________

The asphericity of the third surface is given by the coefficients listedin Table 5D (see below) if the sag X(h) of the aspheric surface at thepoint that is departed from the optical axis by distance h is defined bythe following equation (5D), in which the respective symbols have thesame meanings as in equation (4D).

The lower the refractive index, the lower the temperature at whichoptical materials can be molded to fabricate glass molded lenses.Therefore, using a low-index optical material is desired when making aglass lens by the molding method. In that case, the surface of the lenson the side that is opposite the side where the cemented surface liesmay be rendered aspheric as in Example 2D and this lens design iseffective in correcting chromatic aberration by a sufficient degree tomake it satisfactory as a high-NA objective lens. ##EQU10##

                  TABLE 5D    ______________________________________              r =   -9.585              K =   0.000              A4 =  1.320 × 10.sup.-2              A6 =  -2.520 × 10.sup.-3              A8 =  5.580 × 10.sup.-4              A10 = -5.340 × 10.sup.-5    ______________________________________

FIG. 51 shows a prior art single lens that has an aspheric surface onboth sides and which performs as well as the lens of Example 2D exceptin chromatic aberration. The specific numerical data for that prior artlens are listed in Table 6D (see below) and the associated asphericcoefficients are as listed in Table 7D (also see below). The aberrationsthat develop in the system composed to those data are shown in FIG. 52.Comparing FIGS. 50 and 52, one can clearly see the chromatic aberrationcorrecting effect of the diffraction element.

                  TABLE 6D    ______________________________________    λ.sub.0 = 780 nm f = 3.30 mm NA = 0.55    Surface    No.     r          d      nd      νd                                           n780    ______________________________________    1       Aspheric   2.145  1.58913 61.2 1.58252            surface    2       Aspheric   1.355            surface    3       ∞    1.200  1.58547 29.9 1.57346    4       ∞    ______________________________________

                  TABLE 7D    ______________________________________    1st Surface     2nd Surface    ______________________________________    r =      2.206         r =     -9.585    K =      -0.328        K =     0.000    A4 =     -0.150 × 10.sup.-2                           A4 =    0.132 × 10.sup.-1    A6 =     -0.167 × 10.sup.-3                           A6 =    -0.252 × 10.sup.-2    A8 =     -0.305 × 10.sup.-4                           A8 =    0.558 × 10.sup.-3    A10 =    0.800 × 10.sup.-6                           A10 =   -0.534 × 10.sup.-4    ______________________________________

According to Examples 1D and 2D, objective lenses can be provided thatare of substantially the same size and weight as the prior art asphericlens and which yet are effectively corrected for chromatic aberration.As a further advantage, the portion of those lenses that has arefractive power is a glass lens and, hence, the imaging performance ofthe lenses is completely immune to the effect of humidity changes andsubstantially immune to temperature changes.

EXAMPLE 3D

FIG. 53 shows optical system that uses the hybrid lens according toExample 3D of the present invention. In this example, the hybrid lens isused as a collimator lens in an optical disk apparatus. Plane parallelplate C shown on the right side of FIG. 53 is a cover glass for thelaser diode. The specific numerical data for Example 3D are shown inTable 8D. In the example under consideration, the first surface is anordinary aspheric surface and the third surface is a diffractionsurface. FIG. 54 shows the aberrations that develop in the systemcomposed in accordance with the data listed in Table 8D.

                  TABLE 8D    ______________________________________    λ.sub.0 = 780 nm f = 10.8 mm NA = 0.20    Surface    No.     r           d      nd      νd                                            n780    ______________________________________    1       Aspheric    2.460  1.67790 55.3 1.66959            surface    2       ∞     0.040               1.51653    3       Diffracting 9.000  --            surface    4       ∞     0.250  1.51633 64.1 1.51072    5       ∞     --     --    ______________________________________

The asphericity of the first surface is given by the coefficients listedin Table 9D (see below) if the sag X(h) of the aspheric surface at thepoint that is departed from the optical axis by distance h is defined bythe aforementioned equation (5D).

                  TABLE 9D    ______________________________________              r =   7.231              K =   -0.5933              A4 =  0.000              A6 =  -3.440 × 10.sup.-7              A8 =  -4.370 × 10.sup.-9              A10 = 0.000    ______________________________________

The shape of the third surface is given by the coefficients listed inTable 10D (see below) if the sag X(h) at the point that is departed fromthe optical axis by distance h is expressed by the following equation(6D):

    X(h)=ΔN                                              (6D)

                  TABLE 10D    ______________________________________           N =  INT(2.61 × h.sup.2 - 0.0212 × h.sup.4 + 0.5)           ΔN =                0.001510 × N    ______________________________________

With a high-NA lens, beams of light enter the diffraction elementobliquely in the peripheral portion of the lens and, therefore, comparedto the central portion where almost normal incidence occurs, theperipheral portion of the lens provides a longer optical path even ifthe two areas have the same thickness. Hence, in order to insure thatthe phase difference for each annular segment is the same in both thecentral and peripheral portions, the difference in the thickness of thediffraction element between individual annular segments must be renderedto decrease from the center outward.

Consider, for example, a lens having a comparable NA to that employed inExample 3D; in such a lens, continuity in phase can be assured by makingthe difference in thickness between annular segments in the outermostarea smaller than the difference in the central area by about 1%.However, the discontinuity in phase that occurs if the difference inthickness between annular segments is made equal in the whole part ofthe lens will cause no problem in practical applications. Therefore, inExample 3D under discussion, ΔN is expressed as a linear function of Nand the difference in thickness between individual annular segments isset to be equal in both the central and peripheral parts of the lens.

It should also be mentioned that in the case of a lens like that ofExample 3D which does not have a very large NA, forming the diffractionsurface of a plane surface alone is desired in view of the ease withwhich mold working and shape measurement can be accomplished.

EXAMPLE 4D

FIG. 55 shows optical system in which the hybrid lens of Example 4D ofthe present invention is used as part of a telephoto lens system. Thespecific numerical data for Example 4D are listed in Table 11D (seebelow), in which symbol ω denotes the half view angle and fb the backfocus.

A diffraction element formed of a thermosetting plastic material isjoined to the object side (which is on the left as seen in FIG. 55) ofthe first lens of this telephoto lens system which is positioned theclosest to the object. However, because of the small thickness of thediffraction element, the first and second surfaces are shown to overlapeach other in FIG. 55.

The telephoto lens system under consideration is intended to be used ina wavelength band of 435 to 656 nm and the reference wavelength λ₀ forthe diffraction element at the time of its design is 546.07 nm. FIG. 56shows the aberrations that develop in the system composed in accordancewith the data listed in Table 11D.

                  TABLE 11D    ______________________________________    f = 293.1 mm (at 588 nm)    NA = 2.8 ω = 4.2° fb = 72.40    Surface    No.       r         d          nd    νd    ______________________________________    1         Diffracting                        0.04       1.52249                                         59.8              surface    2         134.989   14.76      1.51633                                         64.1    3         -1430.844 2.20       --    4         113.600   11.80      1.51633                                         64.1    5         525.000   8.98       --    6         ∞   5.50       1.80610                                         33.3    7         178.352   50.0       --    8         86.700    3.00       1.79952                                         42.2    9         42.660    14.80      1.62041                                         60.3    10        496.238   10.42      --    11        -585.886  5.00       1.80518                                         25.4    12        -97.810   3.20       1.58875                                         51.2    13        50.630    60.09      --    14        96.200    6.60       1.69680                                         55.5    15        -80.000   2.70       1.53172                                         48.9    16        113.576   7.00       --    17        ∞   2.00       1.51633                                         64.1    18        ∞   --         --    ______________________________________

The shape of the first surface is given by the coefficients listed inTable 12D (see below) if the sag X(h) at the point that is departed fromthe optical axis by distance h is expressed by the following equation(7D). The effective radius of the first lens is 52.3 mm and its firstsurface is a diffracting surface composed of 133 annular surfaces:##EQU11##

                  TABLE 12D    ______________________________________    N =      INT(4.43 × 10.sup.-2 × h.sup.2 + 1.54 ×             10.sup.-6 × h.sup.4 + 0.5)    rN =     135.029 + 3.58 × 10.sup.-4 × N    ΔN =             -0.001041 × N    ______________________________________

FIG. 57 shows a modification of the telephoto lens of Example 4D, inwhich the hybrid lens positioned the closest to the object is replacedby a single lens having no diffraction element and in which a chromaticaberration correcting filter joined with a diffraction element ispositioned closer to the object than the single lens. The diffractionelement is joined to the image side of the filter. In this case, too,the diffraction element is so thin that the second and third surfacesare shown to overlap each other in FIG. 57.

The specific numerical data for this modified lens system are as listedin Table 13D. The fifth and subsequent surfaces have the same data asthe third and subsequent surfaces in the lens system of Example 4D andthe aberration and other performance characteristics of the two lenssystems are also the same.

                  TABLE 13D    ______________________________________    Surface    No.       r         d          nd    νd    ______________________________________    1         ∞   8.00       1.51633                                         64.1    2         ∞   0.04       1.52249                                         59.8    3         Diffracting                        2.00       --              surface    4         135.029   14.80      1.51633                                         64.1    5         -1430.844 2.00       --    6         113.600   11.80      1.51633                                         64.1    7         525.000   8.98       --    8         ∞   5.50       1.80610                                         33.3    9         178.352   50.00      --    10        86.700    3.00       1.79952                                         42.2    11        42.660    14.80      1.62041                                         60.3    12        496.238   10.42      --    13        -585.886  5.00       1.80518                                         25.4    14        -97.810   3.20       1.58875                                         51.2    15        50.630    60.09      --    16        96.200    6.60       1.69680                                         55.5    17        -80.000   2.70       1.53172                                         48.9    18        113.576   7.00       --    19        ∞   2.00       1.51633                                         64.1    20        ∞   --         --    ______________________________________

The shape of the third surface is given by the coefficients listed inTable 14D (see below) if the sag X(h) at the point that is departed fromthe optical axis by distance h is expressed by the aforementionedequation (6D).

                  TABLE 14D    ______________________________________    N =      INT(4.43 × 10.sup.-2 × h.sup.2 + 1.51 ×             10.sup.-6 × h.sup.4 + 0.5)    ΔN =             0.001041 × N    ______________________________________

FIG. 58 shows a telephoto lens system that has comparable performance tothe system of Example 4D, except that chromatic aberration is correctedby a particular combination of optical materials without using adiffraction element. The specific numerical data for this lens systemare as listed in Table 15D. The aberrations that develop in the systemcomposed in accordance with those data are as shown in FIG. 59.Comparing FIGS. 56 and 59, one can see that if a diffraction element isused, chromatic aberration can selectively be corrected in a veryefficient manner without affecting other performance characteristics.

                  TABLE 15D    ______________________________________    f = 293.1 mm (at 588 nm)    NA = 2.9 ω = 4.2° fb = 72.00    Surface    No.       r         d          nd    νd    ______________________________________    1         140.152   14.80      1.49700                                         81.6    2         -1148.125 2.00       --    3         111.252   11.80      1.49700                                         81.6    4         440.000   10.33      --    5         ∞   5.50       1.72047                                         34.7    6         180.590   49.79      --    7         86.700    3.00       1.79952                                         42.2    8         42.690    14.50      1.62041                                         60.3    9         496.238   9.73       --    10        -585.886  5.00       1.80518                                         25.4    11        -97.810   3.20       1.58875                                         51.2    12        50.630    60.11      --    13        96.200    6.60       1.69680                                         55.5    14        -80.000   2.70       1.53172                                         48.9    15        113.576   8.67       --    16        ∞   2.00       1.51633                                         64.1    17        ∞   --         --    ______________________________________

The foregoing description in Examples 1D to 4D is limited to the casewhere the hybrid lens of the present invention is used either as anobjective or collimator lens for optical disk or as part of a telephotolens system. It should, however, be noted that the hybrid lens is alsoapplicable to other types of optical system unless the view angle isvery wide.

As described above, the present invention combines a glass lens with aplastic diffraction element so as to provide a chromatic aberrationcorrected hybrid lens whose performance is less susceptible toenvironmental changes and to which a diffraction pattern can betransferred in an exact manner.

The following embodiments of the present invention relate to an opticaldevice for correcting chromatic aberration by making use of thereflection and diffraction of light.

According to yet another aspect of the present invention, there isprovided an optical device that is capable of correcting the chromaticaberration that develops in a single lens when the operating wavelengthis offset from the reference value. Stated more specifically, if awavefront aberration (chromatic aberration) occurs in a single lens whenthe operating wavelength is offset from the reference value, thechromatic aberration correcting device of a reflection and diffractiontype according to the present invention cancels that aberration bycreating at a reflecting surface a divergent or convergent wavefront ofopposite nature.

The chromatic aberration correcting device of a reflection andrefractive type according to the present invention may be used not onlyfor correcting the chromatic aberration that develops in a single lensbut also for correcting the chromatic aberration that develops in ahybrid lens. A plurality of lens elements sometimes fails to correctchromatic aberration for various reasons associated with refractiveindex, transmittance, etc. and, especially at short wavelengths nearλ=300 nm, only one type of optical material is available and thecorrection of chromatic aberration is difficult to accomplish. Thechromatic aberration correcting device of a reflection and diffractiontype according to the present invention is capable of correctingchromatic aberration even in such short wavelength range.

In one embodiment of the invention, the contours of the centralreflecting surface and the annular reflecting surfaces in the chromaticaberration correcting device are made circular as seen in a directionperpendicular to those reflecting surfaces and the step distance tbetween adjacent reflecting surfaces is set to be as follows:

    t=λm/2n(m is an integer)

where λ is the reference wavelength within the operating wavelengthband, and n is the refractive index of the reflecting surface on theincident side.

If the correcting device is to be inserted in the optical pathobliquely, the contours of the central reflecting surface and theannular reflecting surfaces may be rendered elliptical as seen in adirection perpendicular to those reflecting surfaces and the stepdistance t is set to be as follows:

    t=Aλm/2n(m is an integer)

where λ is the reference wavelength within the operating wavelengthband, n is the refractive index of the reflecting surface on theincident side, and A is the ratio between the major and minor axes ofthe ellipse.

The value of m desirably satisfies the condition 1≦|m|≦10. The zerovalue of m means a reflecting mirror the surface of which is planar as awhole; therefore, a chromatic aberration correcting device of areflection and diffraction type cannot be fabricated unless m is 1 ormore. On the other hand, if m exceeds 10, a serious disadvantage willoccur under great variations in wavelength in that the proportion oflight of higher-order diffraction increases to lower the efficiency oflight utilization. The sign of the value m determines whether thereflecting surface, taken as a whole, is macroscopically convex orconcave.

If the width of each annular reflecting surface is set to be in inverseproportion to the square of the distance from the optical axis, thewavefront generated upon variation in the wavelength of incident lightcan be made generally spherical. If the lens to be combined is expectedto experience a large change in spherical aberration on account of thevariation in wavelength, it may be corrected by properly adjusting thewidth of annular segments on the reflecting surface in design stage;however, from the viewpoint of wide applicability, it suffices that thewidth of each annular reflecting surface is set to be in inverseproportion to the square of the distance from the optical axis.

The central reflecting surface and the annular reflecting surfaces maycomprise planes that are parallel to one another; alternatively, thosesurfaces may be curved.

The chromatic aberration correcting device of a reflection anddiffraction type according to the present invention is to be combinedwith a lens to correct the chromatic aberration that will occur in thatlens. Stated more specifically, when light having a wavelength differentfrom a reference wavelength enters the lens, it will develop chromaticaberration and in order to correct this aberration, the device of thepresent invention changes the wavefront of the incident light by meansof reflection.

The present invention also provides a chromatic aberration correctingapparatus, in which the chromatic aberration correcting device of areflection and diffraction type described above is inserted in theoptical path between a collimator for collimating the light entering alens and the lens. An exemplary application of this apparatus is tocorrect the aberration that develops in a single lens used for focusinglaser light to form a spot on an optical disk in an optical informationrecording and reproducing apparatus.

EXAMPLES

The present invention is described below with reference to the examplesshown in the accompanying drawings. FIGS. 60 and 61 show the operatingtheory of the chromatic aberration correcting device of the presentinvention.

Reference is first made to FIG. 60. The chromatic aberration correctingdevice of a reflection and diffraction type which is generally indicatedby 311 comprises a circular central reflecting surface 311ac on theoptical axis O and three coaxial circular annular reflecting surfaces311bc, 311cc and 311dc that are located around the central reflectingsurface 311ac. Only three annular reflecting surfaces are shown in FIG.60 but in practice the correcting device of the present invention willbe provided with from 10 to about 100 annular reflecting surfaces. Theprior art diffractive lens has as many as several hundred annularsegments and this is one of the factors by which the chromaticaberration correcting device of a reflection and diffraction typeaccording to the present invention can be distinguished from theconventional diffractive lens.

The circular central reflecting surface 311ac and the circular annularreflecting surfaces 311bc, 311cc and 311dc comprise planes that areparallel to one another and which are offset in position along theoptical axis O by step distance t; taken as a whole, those reflectingsurfaces produce a macroscopically convex shape. For the sake ofclarity, let the correcting device 311 be assumed to be in air (n=1).Also assume that the reference wavelength of light entering thereflecting surface is λ. Then, the step distance t is given by t=λ/2 andthis corresponds to the case where m=1 and n=1 in the equation t=λm/2n.

Consider here the case where plane-wave light (beams of parallel light)having the reference wavelength λ enter the correcting device 311.Adjacent lines 312 indicate the positions taken along the optical pathby the travelling plane-wave light of a specified phase (e.g. 0°) havingthe reference wavelength λ. Since the light having the referencewavelength satisfies the condition t=λ/2, it will remain as a plane waveeven after it has been reflected by the circular central reflectingsurface 311ac or the circular annular reflecting surfaces 311bc-311dc.

Stated in general terms, the optical pathlength difference that occursupon reflection in a medium (refractive index, n; thickness, t) alongthe optical path is given by 2nt. Therefore, if the correcting device311 has step-like reflecting surfaces whose step distance is t asexpressed by t(h)=λ/2n (h is the distance from the optical axis O) or mt(m is an integer), the wavefront of the light having the referencewavelength will in no way change in shape after reflection since if itis reflected by adjacent reflecting areas, the only change that occursto its wavefront is a phase shift of mλ and the reflected light willkeep on travelling without changing its wavefront.

FIG. 61 shows the case where a plane wave having a wavelength λ'slightly longer than the reference wavelength λ enters the correctingdevice 311 which is the same as shown in FIG. 60. The distance betweenadjacent lines 312' is longer than the distance between adjacent lines312 (see FIG. 60) by the shift in wavelength. In the case of reflectionby the correcting device 311, the light that is reflected by thecircular central reflecting surface 311ac travels the shortest distancethrough the medium whereas the light that is reflected by the circularannular reflecting surface 311dc will travel the longest distance. Itshould also be noted that light having a wavelength longer than thereference wavelength has such a nature that the longer the distance ittravels, the more advanced its wavefront is. As a result, the phase ofthe wavefront of light that has been reflected by the circular centralreflecting surface 311ac and the circular annular reflecting surfaces311bc-311dc will lead as a function of the distance from the opticalaxis O and the wavefronts of the reflected light beams will, taken as awhole, be curved to create a single convergent wavefront. In otherwords, the correcting device 311 having step-like reflecting surfacesthat provide macroscopically a shape convex to the ray entrance sidewill cause incident plane-wave light to be reflected as a convergentwavefront if it has a longer wavelength than the reference wavelength.This is equivalent to saying that the light reflection by the correctingdevice 311 will produce a chromatic aberration that cancels off thechromatic aberration that develops in a positive lens having arefractive action and the device can accordingly accomplish thenecessary correction of chromatic aberration.

Conversely, the wavefront of light having a shorter wavelength than thereference wavelength will lag as it travels a longer distance throughthe medium and, hence, it is rendered divergent by the action of thecorrecting device 311. In other words, the correcting device 311 whichhas step-like reflecting surfaces that provide macroscopically a shapeconvex to the ray entrance side will cause incident plane-wave light tobe reflected as a divergent wavefront if it has a shorter wavelengththan the reference wavelength. This is equivalent to saying that thelight reflection by the correcting device 311 will produce a chromaticaberration that cancels off the chromatic aberration that develops in anegative lens having a refractive action and the device can accordinglyaccomplish the necessary correction of chromatic aberration.

Whether the step-like reflecting surfaces to be formed on the correctingdevice 311 produce a macroscopically convex or concave shape depends onvarious factors such as whether the chromatic aberration to be correcteddevelops in a positive lens or a negative lens.

The widths s1, s2 and s3 of the circular annular reflecting surfaces311bc, 311cc and 311dc, respectively, are each set to be in inverseproportion to the square of the distance from the optical axis O.

FIGS. 62 and 63 show an example of the present invention in which thecorrecting device generally indicated by 311A is positioned at an angleof 450 with respect to the optical axis O. The reflecting surface ofthis correcting device comprises an elliptical reflecting surface 311aewhich, as seen in a direction perpendicular to that reflecting surface,is positioned at the center of the optical axis O, and coaxialelliptical annular reflecting surfaces 311be, 311ce and 311de that arepositioned around the central reflecting surface 311ae.

The ratio A between the major and minor axes of the ellipse isdetermined in such a way that each of the orthogonal projections of thereflecting surfaces 311ae-311de onto a plane perpendicular to theoptical axis O will be a circle. In other words, A is 2^(1/2).

If the ellipse defined by the elliptical reflecting surface 311ae isexpressed by (X² /A²)+(Y² /1)=r² (r is a constant) in an XY coordinatesystem, then the step distance t between the reflecting surface 311aeand the adjacent annular reflecting surface 311be and between individualannular reflecting surfaces 311be, 311ce and 311de is given byt=λ·2^(1/2). As in the example shown in FIGS. 60 and 61, thiscorresponds to the case where n=1 and m=1 in the equation t=Aλm/2n (m isan integer). Hence, the example under consideration provides entirelythe same advantage as is obtained in the previous example.

The two examples discussed above concern the case where m=1; if theoperating wavelength range is not very wide, the value of m may beadjusted to 2 or more when determining the step distance t and the lightof mth-order diffraction may safely be used without lowering thediffraction efficiency. Particularly in the case where the width ofannular segments decreases from the center outward, one may graduallyincrease the value of m starting from unity within a single device. Inthis case, the axial distance ΔX(h) of a particular annular reflectingsurface from the central reflecting surface may be determined as afunction of the distance h from the optical axis O by the followingequation:

    ΔX(h)=(m/2n)Int{ r-(1-(1-h.sup.2 /r.sup.2).sup.1/2)/(mλ/2n)!+0.5}

where Int(x) is a function giving an integer not greater than x.

FIG. 64 shows an embodiment of the present invention in which thechromatic aberration correcting device 311A of a reflection anddiffraction type is applied to an optical information recording andreproducing apparatus. Laser light issuing from a laser light source 321is collimated by a collimator lens 322, shaped by a beam shaping prism323 to have a circular cross section and enters a beam splitter 324.Part of the separated laser light is reflected by the correcting device311A fixed on a carriage 334 to enter an objective lens 326. Thecarriage 334 is slidable along guide rails 335 in the radial directionof an optical disk 327 indicated by the two-head arrow in FIG. 64. Thelaser light incident on the objective lens 326 is focused on the opticaldisk 327 and the reflected light from the disk makes reentry into thecorrecting device. 311A which returns it to the beam splitter 324. Partof the return light passes through a lens 330 in signal reproducingoptical system 328 to be supplied into a sensor 332 and the remainderpasses through a lens 331 in servo optical system 329 to be suppliedinto a sensor 333.

Various types are known for the optical information recording andreproducing apparatus that operates in this manner and by combining theobjective lens 326 (which is a single lens) with the correcting device311A, the chromatic aberration that develops in the objective lens 326can be effectively corrected.

On the pages that follow, the present invention is described in greaterdetail with reference to specific examples, all of which are intended tocorrect the chromatic aberration that developed in a positive objectivelens.

EXAMPLE 1E

FIG. 65 shows a chromatic aberration correcting device that has areflecting surface perpendicular to the optical axis O and which isgenerally indicated by 311. The device 311 is adapted to correctchromatic aberration that occurs in an objective lens having thegeometry shown in FIG. 70 and the characteristics shown in FIG. 71. InFIG. 70, the objective lens is indicated by 341 and the referencenumeral 342 denotes an optical disk. Parallel beams of laser lightcoming from a collimator lens are focused by the objective lens 341 toform a spot on the inner recording surface of the optical disk 342;hence, the objective lens 341 is equivalent to the objective lens 326 inthe apparatus shown in FIG. 64.

The objective lens 341 has the following specifications:

    ______________________________________    Focal length            3.3    mm    Operating wavelength,   780    nm    (reference wavelength)    Shift in back focus in response to a                            11     μm/nm    change in wavelength by unit amount,    df.sub.B /dλ    ______________________________________

The numerical data for the objective lens 341 are listed in Table 1E.

The symbols used in FIG. 71 have the following meanings: SA, sphericalaberration; SC, sine condition; S, sagittal; M, meridional. In Table 1E,r_(i) denotes the radius of curvature of an individual lens surface;d_(i), the lens thickness or the aerial distance between individuallenses; N, refractive index.

                  TABLE 1E    ______________________________________    NA = 0.55 F = 3.30 ω -1.7    Surface    No.       r             d      N    ______________________________________     1*         2.168       2.230  1.53677     2*       -6.205        1.363    3         ∞       1.200  1.57346    4         ∞    ______________________________________     *denotes asphericity.

No. 1; K=-0.3265, A4=-0.2263×10⁻², A6=-0.5014×10⁻³, A8=-0.7162×10⁻⁵,A10=-0.3194×10⁻⁴

No. 2; K=-0.9120, A4=0.1648×10⁻¹, A6=-0.5064×10⁻², A8=0.7995×10⁻³,A10=-0.4848×10⁻⁴

The correcting device 311 of Example 1E is intended for normal incidenceand reflection by the obverse surface; if it is assumed that thecorrecting device 311 corresponds to a positive lens having a focallength of 126 mm, the power of the diffractive lens is proportional towavelength and the chromatic aberration that develops in the objectivelens 341 can be corrected. However, if the objective lens and thecorrecting devices are used as two separate elements, a change in theirdistance will cause a corresponding change in the height of rayincidence on the objective lens; to avoid this problem, the objectivelens and the correcting device must be combined, in a unitary assembly.Hence, the correcting device of the present invention is designed tohave a macroscopic shape that is equivalent to a negative lens having afocal length (f) of -126 mm and its reflecting surface is made planar inorder to insure that first-order light will not be subjected to therefractive action of diffraction.

If reflection is obverse surface reflection in air, n=1.0 and to make anegative lens of f=-126 mm on the reflecting surface, the radius ofcurvature must be r=252.0 mm. If a surface having this curvature is madeplanar by providing planes with the axial step distance t being adjustedto λ/2=390 nm=0.390 μm, one can attain both the action of a diffractivelens having f=126 mm and the action of a refractive lens having f=-126mm, thereby insuring that first-order light will travel in a straightpath.

Stated more specifically, X(h), or the axial distance of each of theannular reflecting surfaces 311bc, 311cc and 311dc from the centralreflecting surface 311ac, is expressed in a function of the distance hfrom the optical axis as follows:

    ΔX(h)=(λ/2n)Int{(r-(1-(1-h.sup.2 /r.sub.2).sup.1/2)/(λ/2n)!+0.5}

where Int(x) is a function giving an integer not exceeding x. If thosereflecting surfaces are arranged to provide a macroscopic shapeexpressed by that equation, one can correct the chromatic aberrationthat develops in the objective lens 341. Table 2E below gives data fordescribing the overall shape of the correcting device 311 shown in FIG.65.

                  TABLE 2E    ______________________________________    h (mm)         ΔX (μm)    ______________________________________    0.000 ˜ 0.313                   0.0    ˜0.542   0.39    ˜0.700   0.78    ˜0.829   1.17    ˜0.940   1.56    ˜1.039   1.95    ˜1.130   2.34    ˜1.214   2.73    ˜1.292   3.12    ˜1.366   3.51    ˜1.436   3.90    ˜1.503   4.29    ˜1.567   4.68    ˜1.628   5.07    ˜1.688   5.46    ˜1.745   5.85    ˜1.800   6.24    ˜1.854   6.63    ˜1.906   7.02    ˜1.957   7.41    ˜2.007   7.80    ______________________________________

If the correcting device 311 having this geometry is inserted in thebeams of parallel light between the collimator lens and the objectivelens 314 and if the reflected light from the device 311 is separated bythe beam splitter, defocusing (chromatic aberration) due to thevariation in the operating wavelength of the laser diode can becanceled. In other words, the chromatic aberration shown in FIG. 71 thatdeveloped in the single objective lens 314 can be effectively corrected.

FIG. 69 shows schematically the chromatic aberration that develops inthe objective lens 341 and how it is corrected by the correcting device311. If the incoming laser light has the reference wavelength λ=780 nm,the optical system works properly in that the desired image is picked upby the sensor 322 (see FIG. 64) as a result of processing through theobjective lens 341 and the correcting device 311. In order words, nodefocusing will occur.

However, if the wavelength of the incoming laser light changes to λ=770nm, chromatic aberration (wavefront aberration) as show*n by curve B inFIG. 69 will develop in the objective lens 341. This wavefrontaberration is more or less undercorrected in the peripheral portion ofthe lens. On the other hand, in response to the wavelength shift towardthe shorter range, the correcting device 311 will transform the incidentplane-wave light to produce a divergent wavefront. This divergentwavefront is more or less overcorrected as shown by curve C in FIG. 69.Hence, the two wavefronts cancel each other and the composite wavefrontis such as to produce a desired image in focus. In other words, thechromatic aberration that develops in the objective lens 341 as a resultof wavelength shift can be corrected by the correcting device 311 of thepresent invention.

EXAMPLE 2E

In system of Example 1E, the reflected light from the correcting device311 is separated by the beam splitter and a loss is prone to occur inthe beam splitter. To solve this problem, it is preferred to positionthe correcting device as it is included by 45° with the optical axis asshown in FIG. 64, where the correcting device is indicated by 311A. Inthis case, as already described with reference to FIGS. 62 an 63, thereflecting surface of the correcting device 311A is composed ofelliptical central reflecting surface 311ae and three elliptical annularreflecting surfaces 311be-311de. Considering that the effective phasedifference that is given to the wavefront by one step is sin 45°≃0.707,the step distance t is about 1.41 times as great as the step distanceadopted in Example 1E (1/sin 45°≃1.41). Therefore, the 45° incidencecorrecting device 311A which performs as effectively as the device 311of Example 1E has a geometry that is shown physically in FIG. 66 andnumerically in Table 3E below.

                  TABLE 3E    ______________________________________    along minor axis   along major axis    h (mm)             h (mm)      ΔX (μm)    ______________________________________    0.000 ˜ 0.313                       0.000 ˜ 0.443                                   0.0    ˜0.542       ˜0.767                                   0.55    ˜0.700       ˜.991 1.10    ˜0.829       ˜1.172                                   1.65    ˜0.940       ˜1.330                                   2.20    ˜1.039       ˜1.470                                   2.75    ˜1.130       ˜1.598                                   3.30    ˜1.214       ˜1.717                                   3.86    ˜1.292       ˜1.827                                   4.41    ˜1.366       ˜1.932                                   4.96    ˜1.436       ˜2.031                                   5.51    ˜1.503       ˜2.126                                   6.06    ˜1.567       ˜2.216                                   6.61    ˜1.628       ˜2.303                                   7.17    ˜1.688       ˜2.387                                   7.72    ˜1.745       ˜2.468                                   8.27    ˜1.800       ˜2.548                                   8.82    ˜1.854       ˜2.622                                   9.37    ˜1.906       ˜2.698                                   9.92    ˜1.957       ˜2.768                                   10.47    ˜2.007       ˜2.838                                   11.03    ______________________________________

If the correcting device 311A having this geometry is inserted in thebeams of parallel light between the collimator lens and the objectivelens 314 (between collimator lens 322 and objective lens 326 in the caseshown in FIG. 64), defocusing (chromatic aberration) due to thevariation in the operating wavelength of the laser diode can beeffectively canceled.

EXAMPLE 3E

In Examples 1E and 2E, the reflecting surface is provided on the obversesurface of the chromatic aberration correcting device. However, thechromatic aberration correcting device of the present invention may alsobe constructed as a reverse surface reflection type. FIG. 67 shows anexample of the correcting device adapted for such reverse surfacereflection, which is generally indicated by 311B in FIG. 67. Thecorrecting device of this reverse surface reflection type has theadvantage that its performance is in no way affected if dust or dirt isdeposited on the steps formed on the reflecting surface on the reverseside. In the case of reverse surface reflection, the ratio of operatingwavelength to refractive index decreases in the medium (n>1) and, hence,the step distance t becomes shorter than in Examples 1E and 2E (becausen>1 in the equation t=λm/2n). Table 4E below shows the geometry of thereflecting surface of the 450 incidence aberration correcting device311B that was fabricated from an optical material having n=1.51072.

                  TABLE 4E    ______________________________________    along minor axis   along major axis    h (mm)             h (mm)      ΔX (μm)    ______________________________________    0.000 ˜ 0.313                       0.000 ˜ 0.443                                   0.0    ˜0.542       ˜0.767                                   0.36    ˜0.700       ˜0.991                                   0.73    ˜0.829       ˜1.172                                   1.09    ˜0.940       ˜1.330                                   1.46    ˜1.039       ˜1.470                                   1.82    ˜1.130       ˜1.598                                   2.19    ˜1.214       ˜1.717                                   2.55    ˜1.292       ˜1.827                                   2.92    ˜1.366       ˜1.932                                   3.28    ˜1.436       ˜2.031                                   3.65    ˜1.503       ˜2.126                                   4.01    ˜1.567       ˜2.216                                   4.38    ˜1.628       ˜2.303                                   4.74    ˜1.688       ˜2.387                                   5.11    ˜1.745       ˜2.468                                   5.47    ˜1.800       ˜2.548                                   5.84    ˜-1.854      ˜2.622                                   6.20    ˜1.906       ˜2.696                                   6.57    ˜1.957       ˜2.768                                   6.93    ˜2.007       ˜2.838                                   7.30    ______________________________________

EXAMPLE 4E

The angle of incidence on the chromatic aberration correcting device ofa reflection and diffraction type according to the present invention isin no way limited to 0° or 45°. All that is required is that theorthogonal projections of the central reflecting surface and the annularreflecting surfaces onto a plane perpendicular to the optical axisdescribe shapes that are of a rotation symmetry with respect to theoptical axis which is the center of rotation. FIG. 68 and Table 5E showan example of the geometry of a chromatic aberration correcting device(which is indicated by 311C) that performs as effectively as the deviceof Examples 1E to 3E when the angle of incidence is 300. Since 1/sin30°=2, the step distance t adopted in Example 4E is longer than thoseselected in Examples 1E to 3E; therefore, the correcting device ofExample 4E has the advantage of greater ease in fabrication.

                  TABLE 5E    ______________________________________    along minor axis   along major axis    h (mm)             h (mm)      ΔX (μm)    ______________________________________    0.000 ˜ 0.313                       0.000 ˜ 0.626                                   0.0    ˜0.542       ˜1.085                                   0.78    ˜0.700       ˜1.401                                   1.56    ˜0.829       ˜1.658                                   2.34    ˜0.940       ˜1.880                                   3.12    ˜1.039       ˜2.079                                   3.90    ˜1.130       ˜2.260                                   4.68    ˜1.214       ˜2.428                                   5.46    ˜1.292       ˜2.585                                   6.24    ˜1.366       ˜2.733                                   7.02    ˜1.436       ˜2.873                                   7.80    ˜1.503       ˜3.006                                   8.58    ˜1.567       ˜3.134                                   9.36    ˜1.628       ˜3.257                                   10.14    ˜1.688       ˜3.376                                   10.92    ˜1.745       ˜3.490                                   11.70    ˜1.800       ˜3.601                                   12.48    ˜1.854       ˜3.709                                   13.26    ˜1.906       ˜3.813                                   14.04    ˜1.957       ˜3.915                                   14.82    ˜2.007       ˜4.014                                   15.60    ______________________________________

EXAMPLE 5E

The chromatic aberration correcting device of a reflection anddiffraction type according to the present invention may be provided inportions other than where beams of parallel light travel. In thisExample 5E, the present invention is applied to the reflecting surfaceof a catadioptric lens as shown in FIG. 72, in which the catadioptriclens and the reflecting surface are indicated by 343 and 344,respectively. Numerical data for the catadioptric lens 343 are listed inTable 6E below and the various aberrations that are caused in that lensare shown in FIG. 73, in which d-, g-, C-, F- and e-lines refer to thechromatic aberrations as expressed in terms of spherical aberration, aswell as the lateral chromatic aberrations that develop at the respectivewavelengths. In Table 6E, ν) denotes the Abbe number.

                  TABLE 6E    ______________________________________    F.sub.NO = 1:5.6 f = 44.68    Surface    No.       r        d          N     ν    ______________________________________    1         25.000   3.00       1.77250                                        49.6    2         252.451  1.00    3         -26.100  2.00       1.49176                                        57.4    4         -800.000    ______________________________________

The fourth surface of this lens provides the reflecting surface 344.

The catadioptric lens 343 forms an image at a magnification of 1/6 andwith this lens, the image of an abject lying above the optical axis canbe focused below the axis. However, the lens is unable to achievesatisfactory correction of axial chromatic aberration and at wavelengthsnear 588 nm, df_(B) /dλ is 7.0 μm/nm. In accordance with the theory ofthe present invention, the reflecting surface 344 of the 2F2 lens 343 isformed of annular segments and the thus formed surface is capable ofcorrecting the axial chromatic aberration that develops in the lens 343.In other words, the reflecting surface 344 is adapted for normalincidence and reflection by the rear surface (which is equivalent to thedevice shown in FIG. 65 except that the reflecting surface is adaptedfor reverse surface reflection as in the device shown in FIG. 67). Table7E below shows the geometry of the reflecting surface 344 of the lens343 that was fabricated from an optical material having n=1.49176.

                  TABLE 7E    ______________________________________    h (mm)        ΔX (μm)    ______________________________________    0.000 ˜ 0.59                  0.19    ˜1.02   0.39    ˜1.32   0.59    ˜1.56   0.78    ˜1.77   0.98    ˜1.96   1.18    ˜2.13   1.37    ˜2.29   1.57    ˜2.44   1.77    ˜2.58   1.96    ˜2.71   2.16    ˜2.84   2.36    ˜2.96   4.56    ˜3.07   2.75    ˜3.18   2.95    ˜3.29   3.15    ˜3.40   3.34    ˜3.50   3.54    ˜3.60   3.74    ˜3.69   3.98    ˜3.79   4.13    ˜3.88   4.33    ˜3.97   4.52    ˜4.06   4.72    ˜4.14   4.92    ˜4.22   5.12    ˜4.31   5.31    ______________________________________

The reflecting surface having this geometry is capable of correcting thechromatic aberrations shown in 25 FIG. 73.

As described on the foregoing pages, the chromatic aberration correctingdevice of a reflection and diffraction type according to the presentinvention is fabricated from a single reflecting element and it yet iscapable of effective correction of the chromatic aberration thatdevelops in a lens being used in combination with that device. Since thereflecting element is used extensively in optical system, one only needprocess this reflecting element to fabricate the chromating aberrationcorrecting device of the present invention and, hence, the desiredcorrection of chromatic aberration can be achieved without adding anyspecial optical elements. Furthermore, if the correcting device is usedon an optical information recording and reproducing apparatus,defocusing due to the variation in the wavelength of laser light can becorrected by a low-cost system layout.

I claim:
 1. A lens element having a diffractive surface, saiddiffractive surface being formed to correct simultaneously chromaticaberration and spherical aberration generated by said lenselement,wherein said diffractive surface has a convex aspheric shapemacroscopically and has a radius of curvature that increases withdistance from an optical axis.
 2. A lens element having a diffractivesurface, said diffractive surface being formed to correct simultaneouslychromatic aberration and spherical aberration generated by said lenselement,wherein said diffractive surface has a convex aspheric shapemacroscopically and has a radius of curvature that increases withdistance from an optical axis and wherein said diffractive surface ofsaid lens element comprises annular steps formed on a first surface ofsaid lens element and each of said annular steps has an aspheric annularsurface.
 3. A lens element as claimed in claim 2, wherein the shape ofsaid diffractive surface is defined by the following equation: ##EQU12##where X(h) is the sag of said diffractive surface, h is the radialdistance of a point on said diffractive surface from the optical axis, ris the radius of curvature of the vertex of the aspheric surface, N isthe number of the step, K is the conic constant, A4, A6, A8 and A10 areaspheric coefficients, and Δ_(N) are constants.
 4. A lens element asclaimed in claim 1, whereinsaid diffractive surface comprises annularsteps, and a thickness of said lens element decreases with distance froman optical axis except at transition points of said annular steps, thethickness increasing abruptly at said transition points.
 5. A lenselement as claimed in claim 4, wherein said lens element satisfies thefollowing relationship:

    0.8≦t(n-1)/λ≦10

where λ is the wavelength of light being corrected by said lens element,t is the shift amount in the optical axis direction at a correspondingone of said transition points, and n is the refractive index of themedium of which said lens element is made.
 6. A lens element as claimedin claim 5, wherein said diffractive surface has a greater curvaturethan a second surface of said lens element which opposes saiddiffractive surface.
 7. A lens element as claimed in claim 1, whereinsaid diffractive surface has a lesser curvature than a second surfacewhich opposes said diffractive surface.
 8. A lens element as claimed inclaim 3, wherein each of said aspheric annular surfaces has a curvaturedifferent than the curvatures of other ones of said annular surfaces. 9.A lens element as claimed in claim 8, wherein each of said asphericannular surfaces is rotationally symmetrical with respect to the opticalaxis.
 10. A lens element as claimed in claim 4, wherein a second surfacewhich opposes said diffractive surface is a continuous aspheric surface.11. A lens element as claimed in claim 1, wherein said diffractivesurface of said lens element comprises a plurality of ring shapedsurfaces, and a second surface of said lens element is a continuousaspheric surface.
 12. A lens element as claimed in claim 4, whereinheights of said transition points from the optical axis are defined bythe following relationship:

    N=INT(Ah.sup.2 +Bh.sup.4 +C)

where N is an integer designating the number for the annual step ascounted from the optical axis, h is the height of said transition pointsfrom the optical axis, and A, B, and C are constants.
 13. A lens elementas claimed in claim 1, wherein the shape of said diffractive surface isdefined by the following equation:

    X(h)=ΔN

where X(h) is the sag of said diffractive surface, h is the radialdistance of a point on said diffractive surface from the optical axis,and

    ΔN=D*N

where D is a constant and N is the number for the annual step as countedfrom the optical axis.
 14. A lens element having a diffractive surface,said diffractive surface being formed to correct simultaneouslychromatic aberration and spherical aberration generated by said lenselement,wherein said diffractive surface has a convex aspheric shapemacroscopically and has a radius of curvature that increases withdistance from an optical axis, and wherein said diffractive surface hasa greater curvature than a second surface of said lens element whichopposes said diffractive surface.